Great/Big - Interchangeable?

Hello there, folks.

I'm Dutch, and I'm studying English language. I had to hand in an autobiography a couple of days ago, and the teacher said one of my sentences was wrong.

"Music is my greatest interest."

That's how she wrote it on the blackboard anyway, the sentence was actually "I have a lot of interests, and music is one of my greatest". The teacher then went on about how the usage of "greatest" here is wrong, and that it should be "biggest". She said the two words aren't interchangeable. This kind of puzzled me, I'm sure I've seen it before.

I'm not trying to prove my teacher wrong, but I'm just so confused and I'd like to have this cleared up. So, are "greatest" and "biggest" interchangeable or not? Is the sentence I wrote down really incorrect?

Thanks~
- Joshua Mononoetoe