"It is my teacher."
Translation:Це мій вчитель.
It's not "more correct" (what's "more" correct? xD), it has a different meaning. One can say "Hi, it's me", right? Doesn't mean I'm an "it" :) Or "It was you all along!"
But I do agree that as a "primary" translation I'd put "this" because that would be less dependent on the context: "This is my teacher" sounds like a introducing sort of "informational" sentence, and not as an answer to "Who's in the kitchen? It's my teacher" :D
There is no difference, they both mean the same.
The Ukrainian language has this kind of flexibility with some words, where you can exchange в and у to achieve a more melodic sound.
For example, if you want to say "to the teacher", you would rather say "до вчителя" rather than "до учителя". In the second one we have two vowels in a row which is not so pleasant to pronounce. Besides, when talking fast, this "о у" part will sound close to "о в" anyway.
The opposite example, "my teacher" is better as "мій учитель", consonant-vowel-consonant. "Мій вчитель" is quite tough to pronounce, and if you do, "в" kinda softens and turns into "у" by itself.
I hope my explanation is not too confusing :)