If it's any consolation, they probably take their own statements less literally than you do, and so it's less important that they're incoherent than you might think. They'll mostly end up acting and deciding by copying others, which works pretty well in general (see: The Secret Of Our Success).

Obviously I have much less information about your situation than you, but it seems to me that you're not in the right here, and you should be less adversarial.

E.g.:

Yesterday, a teacher was explaining the composition of a literary essay, and she claimed that an essay writer isn't required to provide justification for their claims. I asked, "Then why should I believe anything the essay says?" and she replied, "You're free to decide whether you believe it or not," and I was just too exhausted from last week to explain that's not how beliefs should work.

But an essay writer isn't required to provide justification for their claims. For example, your first sentence is a claim that you have started studying creative writing full time. Have you justified this to me (either in some unattainable absolute sense, or even just beyond reasonable doubt)? No. Should you? Also no.

When you run into an absurd claim like "An essay writer isn't required to provide justifications for their claims," you should think seriously about how it might be true. I think you're only going to be satisfied by understanding communication on a more detailed level than your professors do, but you should do that, not just reject what they say.

Back to the object level: Why should I believe you when you claim that you've started studying creative writing? I do believe you, of course - but practically speaking, why do I do that? Try to figure out an answer that generalizes by being based on the practicalities of how humans communicate and infer things about the world. And then apply that answer back to what sort of evidence an essay writer needs to provide to their audience to do their job well.

I also think you're trying to use arguments in ways that won't work. Robert Nozick makes some clever comments about arguments in best part of his book Philosophical Explanations (the introduction), something like: The goal of most philosophers seems to be to find arguments so compelling, that if a person were to disagree with the conclusion after reading the argument, their head would explode.

Longer quote:

The terminology of philosophical art is coercive: arguments are powerful and best when they are knockdown, arguments force you to a conclusion, if you believe the premises you have to or must believe the conclusion, some arguments do not carry much punch, and so forth. A philosophical argument is an attempt to get someone to believe something, whether he wants to believe it or not. A successful philosophical argument, a strong argument, forces someone to a belief.

Though philosophy is carried on as a coercive activity, the penalty philosophers wield is, after all, rather weak. If the other person is willing to bear the label of "irrational" or "having the worse arguments," he can skip away happily maintaining his previous belief. He will be trailed, of course, by the philosopher furiously hurling philosophical imprecations: "What do you mean, you're willing to be irrational? You shouldn't be irrational because..." And although the philosopher is embarrassed by his inability to complete this sentence in a noncircular fashion - he can only produce reasons for accepting reasons - still, he is unwilling to let his adversary go.

Wouldn't it be better if philosophical arguments left the person no possible answer at all, reducing him to impotent silence? Even then, he might sit there silently, smiling, Buddhalike. Perhaps philosophers need arguments so powerful they set up reverberations in the brain: if the person refuses to accept the conclusion, he dies. How's that for a powerful argument. Yet, as with other physical threats ("your money or your life"), he can choose defiance. A "perfect" philosophical argument would leave no choice.

But the point of that chapter is that such arguments don't exist. They're an oversimplification of how arguments work. A fiction. Much like an essay, an argument with a professor is an exercise in communication, not in structuring a coercive argument.

So if nothing else, I think taking a more learning-oriented approach towards your professors might make you more likely to be able to convince them of things :)

You could try to explain your perspective:

A.

Here are some of the benefits to communication:

"Objectivity"* 'There are at least three sides to every debate - yours, mine and the truth.'

1) figuring out if we agree or disagree with each other (which may be more difficult if we don't share a language. If we use different words for the same things that's confusing).

2) You and I may both be right and wrong (because we believe more than one thing). If we both ignore each other and don't operate in good faith, we may learn nothing from each other, despite how much we can learn from each other.

B.

1) Resolution. Do disagreements between people have to last forever, or do we think it better when they do not? Even if we did disagree with someone about something for a long time, finding common ground might be good/useful.

Perhaps if we look at a lot of philosophy, we will find a lot of truth/good stuff and false/not very good stuff from the same author/school of thought. Being able to engage with different views, and see through them (peer through the lens), and also see through them (there's a smudge on these glasses/these sunglasses make it easier to see when the sun is too bright (perhaps a 'subjective or objective' phenomenon), but hard at night). Rather than tying ourselves to one rock, why not see the whole mountain?

(Explanations involving the notion "holistic" may be useful, but I haven't gone down that road.)

2) It's good to learn from more than one source. (Through one lens what everyone agrees on is probably right. Through another, widespread agreement indicates error - perhaps a result of widespread censorship or lack of engagement.)

3) The people you're talking to have strong moral opinions on some issues?

C.

Distinguish areas which have answers from areas which don't:

You and I may both like different flavors of icecream. Which is better depends on the person (or perhaps their tongue). In matters of taste...

Someone can choose to smoke if they wish. But being aware of its strong negative impacts we might hold some things to be (especially) wrong, including: forcing people to smoke.

(Morality is where things get complicated.)

*What is "objective"? What is seen through a human eye, or what is seen through a cat's eye, or what is seen through a telescope?

Objective is what is there.

Objective is what a human eye sees in an art gallery, and what a cat sees. For a particular art gallery, a human may see tapestries, while a cat may see loose threads they can pull if they climb up there.

(There are alternatives to 'objective', perhaps those you disagree with reject the notion of the 'one eye', rather than 'the true thing which is seen'. Perhaps using fancy words won't help.)

If you have a friend that shares your taste in music, and they recommend an album, it's probably going to be good. If you recommend things to each a lot, maybe these recommendations are not always good, but usually good - and sometimes they're amazing.

Perhaps when your tastes in music diverge in an area where they overlap it is interesting to learn why. (Not all things (that are interesting) are easy to put into words.)