Is it normal i love writing but hate school-assigned writing?

Once you make a hobby a job it loses its luster. Thus it just becomes a job.

I love writing stories, poems, and songs. I also love doing art but every time a teacher makes it a requirement, it'd seem like i lost all the skills i have which pisses me off.

School writing is uncreative and very square as you have to follow rules but with your own writing you can be creative and make something outside of the box.

Perhaps performance anxiety is part of what's going on?

It's one thing to write for an invisible audience who may or may not critique your work, and something very different to write something with the knowledge that someone you know will read and judge it.

If you're going to write stuff for others to read, you have to accept that the world is full of critics, and you have to learn how to deal with them. That can be difficult because criticism is never pleasant, but it might be helpful to cultivate the mindset that it's all just opinions, and it may or may not contain useful nuggets which could improve your writing

I thought that I hated writing and couldn't do it at all, until I started writing outside of school.

Yep, me too mate!