Pretty much if you can build a list of traits that make a story bad and say "you did this number of them and it's not funny" then it's a safe bet that the story is bad.

The Name of the Wind is still enjoyable even though the main character is a giant Stu. Everything that happens to him builds him as a legend.

"What's good or bad is based only on opinions, not facts."

Okay, so why is Shakespeare's poetry enjoyed by people everywhere, while my silly doggerel about my cat hasn't even been published in the school paper?

Why is it that people commonly criticize "Twilight" as being poorly written, but not "Dracula"?

Why can your high school literature teacher justify giving you a bad grade for poor writing, even if your grammar and spelling are fine?

The fact is, people judge each others' writing all the time. Book critics make a living from doing it.

And there's a difference between judging quality and judging preference. "Pride and Prejudice" is a very well-written book. Many people really enjoy it. I don't; I find it rather tedious to read. But I can recognize good writing when I see it; it's a well-written book, even though I don't like the genre. On the other hand, even though I absolutely love fantasy and sci-fi, I recognize "Eragon" as rather bad writing, a teenager's first attempt that somehow got published.

I also recognize that bad writers grow out of it. Christopher Paolini is probably going to write very well when he's had more practice, if he doesn't get a big head about having been published so young. But how is a person to know how to improve their writing if everyone says, "Well, it's only my opinion, but I personally happen to dislike your work," rather than, "Your characters have no realistic motivations, and your heroine is flatter than a cardboard cutout. You need to fix that"?

Saying I enjoy a piece of literature, and saying I think it's well-written, are two different things. I can read "A Little Princess" and admit that Sara Crewe is a Mary Sue while still enjoying the book thoroughly. I can wade through fifty pages about the Paris sewers and still enjoy "Les Miserables".

If we don't critique each others' writing, how are we ever going to get any better at it?

That argument applies to a lot of things, but not quality. Some people don't like some genres. I myself can't stand and don't read horror and tragedy. However, this is entirely separate for how good the thing is, and it's a poor reviewer indeed who mistakes their personal dislike for shoddy construction.

Also, say we assume that everything is based on opinion. You posted it to a public forum, thereby exposing it to the judgement of others, and they have judged that writing needs to follow certain rules to be acceptable. If they judge that your story does not follow these rules, then you should accept their opinion. If you really wanted only your opinion to matter, then you probably shouldn't have put it under others' scrutiny.

Sure, some of what's good or bad is pretty subjective. If we're targeting your story, though, we're not doing it because it's mostly competent and we just don't like the direction it's heading. We're doing it because it contains glaring problems in the building blocks of the story: characterisation (especially in characters from canon), world-building, sentence structure, plotting and pacing, among others. These aren't subjective; they're objective standards, and to get our attention, you need to have failed them pretty hard.

((Some of that might come across as a bit rude. :-( But I think that's the general message we need to get across.))

Dear writer: The rules of writing are not arbitrary!

If you try to make brownies with rhubarb jelly instead of eggs, we have every right to (a) not eat it, or (b) if we do, say we don't like it. If you try to hold a house together with glue instead of nails, we have every right to laugh at you when it falls apart and point out that nails would have held it together better, so you don't make the same mistake again.

Just like the rules of brownie-making say you need eggs and the rules of house-building say you need nails, the rules of writing say you need SPaG, a coherent plot, and a grasp of characterization. This is for a reason: it makes your story hold together and appeal to more people, just like eggs make brownies hold together and taste good; just like nails make a house hold together and not come crashing down on your head. It is not merely a matter of opinion.

~Neshomeh

Good and bad could be something subjective, however, if your story do something like turning a character who is pure good into a genocidal maniac without a credible reason, or that your 'writing' consists of blind plagiarization of canon with badly-thought additions, you could at least ask yourself some questions.

Granted, failing at that level is pretty rare, but the fact is that there is some elements which will show your writing under a bad light, no matter the opinion. Some things just cannot be done. Besides, writers are always the wort type of judges when their own work is concerned, hence the concept of beta-reader.