Interesting question! I think you're right that there's something peculiar about this disjunctive syllogism:

(1) B v ~ B
(2) ~ B
(3) ~ B

You say that (2) must be the negation of (1)'s left disjunct rather than the assertion of (1)'s right disjunct, even though both of those are syntactically the same. You may find allies in those who distinguish between (i) denying or rejecting a proposition and (ii) asserting the proposition's negation. See Section 2.5 of this SEP entry.

But here's a different diagnosis. Although (1)-(3) is a valid argument, and even a valid instance of disjunctive syllogism, the argument is informally defective because premise (1) is superfluous: (1) isn't needed for the argument's validity. Furthermore, anyone justified in asserting (2) is thereby justified in asserting (3) without need of (1). This argument is similar:

(4) ~ B v B
(5) ~ ~ B
(6) B

The claim that (5) is the negation of (4)'s left disjunct is at least as plausible as the claim that (2) is the negation of (1)'s left disjunct. But maybe the better diagnosis is that (4)-(6) is informally defective because (4) is unnecessary for the argument's validity and unnecessary for rationally proceeding from (5) to (6).

Like you, I'm puzzled by the form of the conditional "Only if A, then B." It doesn't seem to be idiomatic English. One might say "Only if you go to the party will I go," but one wouldn't say "Only if you go to the party, then I will go." That would be unidiomatic. So I presume that the conditional form you're learning is "Only if A, B" rather than "Only if A, then B." I would interpret "Only if A, B" as stating that A is a necessary condition for B, and therefore implying that B is a sufficient condition for A.

If one wants to say that A is both necessary and sufficient for B, then one can say "If and only if A, B" -- although "A if and only if B" would be a smoother way of saying it. In any case, make sure that your logic teacher really did say "Only if A, then B" and, if so, ask if he/she meant to say "Only if A, B."

When you say you are a determinist, that could mean various things. It might mean that the world is governed by deterministic laws, but by itself that doesn't answer the question of whether we are free or morally responsible. Incompatibilists say that determinism in this sense rules out freedom; compatibilists disagree. There are interesting arguments on both sides. I suspect that what you're actually saying is that you think determinism is true and you are an incompatibilist. You think that if determinism is true, we aren't free, and you worry that if we aren't free, we can't be responsible for what we do. But there's a lot packed in here.

Though I'm not interested in making a fuss about it, I'm intrigued that you are "personally a determinist." There's a difficult and interesting debate about whether quantum mechanics is deterministic or indeterministic. Once again, there are interesting arguments on both sides. My own view is agnostic. If I had to pick, I'm inclined to the side that sees the quantum world as indeterministic, but I don't think I'm in a good position to have a firm opinion. Are you?

In spite of that, I'm quite comfortable believing that some things are right, some are wrong, and that we're at least sometimes responsible for which we end up doing. I'm not comfortable (not philosophically comfortable, I mean; I don't lose sleep over it) with the idea that questions apparently so far removed from difficult physical and metaphysical debates should be hostage to those debates. I'm much more confident that there are good people whom we appropriately admire and not-so-good people whom we appropriately don't admire than I am about long chains of subtle reasoning meant to connect very different domains. I'm what some might call a Moorean (after G. E. Moore) about moral judgments. I think it's appropriate to be much more confident about many of those than about skeptical claims based on complicated tangle of physics and metaphysics and God knows what else. But to the extent that I look at things this way, it inclines me to a kind of compatibilism. Since I'm much more convinced of what I've said about morality than I am about physical determinism or indeterminism, I'm inclined to say that morality presupposes neither of those things. And though it might make some people think I should have my Philosopher's League membership revoked, I think it's fine to hold a view like this without a theory to go with it.

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All that said: I would point something else out. It's one thing to say that the physical laws are deterministic. It's another to say that I was "destined" to make the choices I made. Even if determinism is true, that leaves a lot unsettled, not least whether laws of nature compel us to behave as we do, and, for that matter, whether physics even provides the right intellectual tools for thinking about what it means to make choices.

Funny you should ask. It's grading season and I've spent a chunk of my day reading essays by freshmen. Some are pretty well-written; others not so much. I'm with your prof.

If I sent a paper full of bad grammar to a philosophy journal, it would either be rejected or, if it was otherwise worth considering, would be sent back for revision. You can think of either of these as the professional equivalent of getting points knocked off.

But aside from what happens in the profession, I don't see my role as narrowly as you think I should. Part of the point of my essay assignments is to improve their strictly philosophical skills. But I take it to be part of my job to help students learn to write better essays in general. I don't think that this falls only to the writing teachers in the English department; I don't have that sort of siloed view of a university education.

I'd add: experience suggests that ungrammatical prose often goes with careless or even muddled thinking. And it makes it more likely that the reader will misunderstand or (a different matter, but still...) get annoyed and just stop reading.

If it makes you feel any better, if you submitted a paper to me that showed philosophical insight, careful thought, and overall clear expression, I would dock you not at all for a handful of minor grammatical lapses. But if it rose to the point of being annoying, I wouldn't give you as good a grade as I would have if you not only were doing good philosophy but also had produced a better essay.

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And by the way: if I were grading your question, I might suggest that you re-write it, perhaps this way:

Hi, I'm a college freshman taking my first philosophy class. My professor takes points off for grammatical mistakes. I disagree with this approach. Aren't the ideas the most important thing, especially for philosophy?

That way, your reader will pay attention to what you say, and not to lapses in the way you say it.

Grammatical mistakes in a student's paper get in the way when I'm trying to follow what s/he's saying. If you want to persuade someone of something, don't distract them. Bad grammar (and more generally, bad writing) can be very distracting.

There is an interesting and much-discussed piece by Richard Hare called "Nothing Matters", in R. M. Hare, Applications of Moral Philosophy (London: Macmillan, 1972), pp. 32–47). Hare develops the point that 'My wife matters' does not have the same sort of logical grammar as 'My wife chatters.' The idea is that chattering is something that my wife does to or at me, whereas mattering is not, in spite of the fact that 'My wife chatters' might be said when my wife chatters to me. Mattering is not like a sort of radiation, like invisible blue light, say, only more rarified, which my wife emits. A lead shield between me and my wife would not prevent her mattering to me. There are difficulties, certainly, with Hare's non-cognitivist approach, but his piece might be the best place for you to start.

I've come to the conclusion that you may be confusing "has their own opinion" with "has their own truth."

2 plus two is 4, whether someone believes it's 5 or not. If they believe that it's 5, this is their (very confused) belief, but what in the world do we gain by saying that it's their truth? If you talk that way, you blur the useful distinction between being right and being wrong.

It gets worse. If I take you seriously, then I could respond by saying "well it may be your truth that everybody has their own truth, but it's my truth that they don't. And so if you want me to take you seriously, you've given me a perfect reason not to take you seriously.

Of course people have different beliefs. We usually take that to be a matter of people disagreeing. But if you and I genuinely disagree, and aren't just play-acting or using words for fun, we can't both be right. And if either or both of us is wrong, then at least one of us doesn't have the truth of the matter; we have a mistaken belief about the subject of our disagreement.

Now you might ask: who has the right to say who's right or wrong? But that's the wrong question. The world doesn't give a darn what I think about it. The world is the way it is whether I or anyone else know what that way is. Reality isn't up to us. It seems to please some people to think otherwise, but it pleases some people to pick the anchovies off their pizza; there's no accounting for tastes.

In asking the questions you've asked, you presuppose that there are correct answers. Otherwise, why bother? Why not just come to a belief and call it your truth? Asking a question seriously doesn't fit with thinking that "everyone has their own truth." Asking questions seriously supposes that there are answers, and that it's possible to get those answers wrong. Most of the time, that's what most of us think. It's hard to see why we should think otherwise.

One needn't know who first coined a word or even how it was originally used for that word to be meaningful, and similarly the fact that the origins of ancient artworks are murky doesn't entail that they are without meaning. The original meaning may be lost, but new meanings are generated, often retaining traces (often more) of earlier meanings. Now, of course, some words are more commonly understood than others, and there are lots of artworks that hold generally shared meanings for people. Sublime landscapes, beautiful portraits, and rousing political artworks support common interpretations galore. So, it seems pretty clear to me that meaning is transmitted and shared through artwork. Sure, when pushed different people generate different shades of meaning and different connotations when asked about how they understand words, but the agreement, facility, and approval with which people share word usage points to shared meanings. And some words are understood only within recondite discourses by small audiences scholars and technicians. So it is with a some artwork, especially the most avant garde and experimental. Poets often twist and strain the meaning of words, which can make shared meaning difficult, but often not impossible to tease out. The meaning of paintings is the product of a conversation between the painter, the audience, and critics, as well as other painters. That meaning can change over time, or not. I might add that I think, just as it is with words, it's not exactly right to speak of a single meaning for an artwork. One remarkable property of good art, like powerful language, is how fecund it is, how much meaning and different meanings it generates.

In cases where the celebrity has intentionally established a false perception that was consciously used to leverage considerable benefits, especially financial benefits, the celebrity owes an apology, at least, to the public (perhaps also resigning from a position, perhaps returning goods). There's a kind of fraud in that. But the responsibility is limited for two reasons: (1) most people commonly try to present themselves in an optimal way and (2) everyone understands that. The point at which legitimate grooming shades into fraudulent deception can be difficult, but those with experienced judgment in the relevant contexts are best suited to draw the line. Neither the public nor the media have the right to examine anyone's private life, and that includes the private lives of celebrities. Except when special circumstances prohibit it (say teacher-student relationships), people do have a right to criticize others and even to expose others when the information about those matters exposed was obtained in permissible ways or when there's an overriding public interest in doing so. So, for example, if a journalists were to have invaded a celebrity's privacy inappropriately, discovering evidence of the celebrity's involvement in a plot to murder someone, the journalist would face a duty to inform the relevant authorities. Information about a child or spouse's drug addition or consensual sexual conduct or past peccadillos would, however, be off limits.