"NO, YOU CANNOT DO THAT"

I have this thing that when someone told me I'm not capable to do something, it makes me want to do it.
As someone who is a littlw perfectionist, I dislike being told about what I'm not capable of.
I can't remember exactly when I started being like this. The first event that I remember is when I was in Math class, last year of high school.
We had same teacher as when we did the year before. I never liked Math, never paid attention or did any works.
But it was our last year in high school and our grades were (kind of) determining whether we're going to graduate or not. And maybe the teacher was even more anxious than the students so he started teaching more seriously.
One day, he told me to solve a problem on the whiteboard. I told him I can't, because I don't understand.
(Yeah, I've always been that frontal >_>)
He raised his eyebrows (he's not the type that yell and mad and do all scary teachers do, btw) and smirked, "This is very easy and you can't solve it? Tsk tsk. Go sit then."
I felt bad. Either it was because I felt belittled, or guilty, or ashamed of my self.
But I replied to him, "Fine, I'll solve this. Give me 5 minutes!"
Then I went to my smartest friend in class and learned from her.
The result? I did it correctly and since then, I did every single homework, solved most of given problems, did all exams by myself, and got 9.75 in the final exam (even higher score than my English score!).

The most recent is when I told my mom I'm going to pay for my brother's college tuition. And she (and my stepfather) told me to not to. Because they thought I'm not able to keep that kind of commitment. They're afraid I'm going to fail in midways and will leave my brother helpless.
My reaction was "No. I'm going to pay. I don't care if you think I can't, but I'm going to and I will commit until he graduates."

It's a shame that people need to belittle me to make me stand taller and do better, really haha. Maybe all I need is a little motivation and the satisfaction feeling of proofing people's bad thoughts about me are wrong.
The problem is, I don't always meet people telling me like that. So while that kind of people isn't around, I need to find a better motivation to keep on going.