Difference between would and will
(AmE, non-linguist) It's a little tricky to say would is the past form of will, as will is an auxiliary verb that doesn't conjugate normally. It does work with will as the wish meaning. Here is part of the problem, I think.
Will for the future is correct. I will go to MIT in 2 years.. If someone says I would go to MIT someday without further elaboration, I think it's not formally "correct", but just the informality of the spoken word.
The "correct" use is
*I would go to MIT if (I had the chance, the money, got in, etc.)
But I can see someone kind of saying it casually/thoughtfully
I would go to MIT. It sounds like a good thing to do.
Used to express a desire/wish, it's more in the form of
Would that I were employed and financially independent. I hate living at home still. - or I would love to live independently. (Implied: if only I could.)
Why would vs will? Will is more concrete, less conditional. I will love living on my own does not mean the same thing. It may be different for you, but in the US, will is something we ask youngsters, who have the optimism of youth:
What will you be when you grow up? Typical answer: I'm going to be a horse trainer/veterinarian/scientist/doctor/nurse/teacher/mother/father/truck driver/fire fighter/movie star, etc.
As we age, wills become woulds.
I would like to be a musician/writer/lawyer/activist/therapist, etc.
It is also seen as a less presumptuous/prideful way to express a desire. It's called a softening word.
(college student:) "I'm going to be a doctor." (Other college student:) "In your dreams! Do you know how hard it is to get into Med School?"
vs.
(college student:) "I would like to be a doctor. I hope I get in (-to Medical School.)" (Other college student:) "Yeah, so would I. That would really be great. Hey, do you want to study together?"
"This really annoys me a lot."
Yeah, I know plenty of people that let the way others speak really bother them. It drives me crazy when people say drownded or real-a-tor. Don't let on, though. It's not cool. I would (<- softening word) try to accept this as a foible of your adopted culture. Que sera and all that. Having a pre-planned reply to a particular annoyance might help. (Would you? Tell me a bit about that.)
Good luck, and welcome to EL&U. We are happy to answer questions about English.
You are/were right. Your friend who says "I would go to MIT someday" is wrong, unless there is some condition applied (or implied). For example, s?he might reasonably say, "I would go to the zoo someday if there were a bus that passed by it."
(Note that this is different from "I will go to the zoo someday if there is a bus that passes by it.")
But I would suggest this, which might help: The next time you hear someone say "would" in a context where it sounds odd to you, ask about it. The person will perhaps explain what s?he means and why it makes sense. After two or three such incidents you should have a more solid feeling for what is meant and when you can use "would".