At the beginning of 8th grade, I made a bold statement to my cousins: I was going to be the top student in the class that year. Immediate mockery ensued, and for most of that year, some of my cousins would consistently make fun of my bold claims.
The idea of me achieving something like that was not very crazy, I had ranked 3rd in class in 4th grade, 6th in 6th grade and 3rd in 7th grade. In 7th grade, the difference in score between the student who ranked 1st and 2nd was a long one. But the difference between the person who ranked 2nd and myself was not significant. In 8th grade, the superstar student who had ranked 1st was no longer there (she switched to a better school). So I had calculated that the odds of me outworking the remaining competition were good, and I could easily score better than the next person, and that would put me 1st.
My cousins had a very different perception of me. You see, I wasn't the kid who was super interested in school. I preferred staying home rather than going to school. By the end of third grade, I had announced that I would not be going to school anymore (And YES, I did end up skipping a whole year, but was homeschooled of sorts). I was THAT kid. I made life particularly difficult for my parents. I was the kid who got what he wanted. So I had a pretty bad reputation in my cousin circle from that perspective.
Even when I went back to school for 4th grade, I wasn't particularly interested in studying, but I was somewhat book smart. I skipped school most of the time, and my mom would get notes copied from a classmate and read them to me.
Back to the mockery. I had made this bold statement, and I had to prove myself and follow through or risk the embarrassment for the foreseeable future. This kindled a fire in me. I consistently put in a generous amount of work for every test, every assignment, every exam. I had set this vision for myself, and I was following through with daily actions. In the end, I did end up placing top of the class that year! The day it was announced, I remember my cousins coming over. And I heard complete silence from them. I was vindicated. All the taunting endured and hard work performed was all worth it in that moment.
In the end, it's not to prove things to others, but to prove what you're capable of to yourself. Leverage the power the haters, the keyboard warriors, and trolls give you and use it to propel yourself forward. And don't forget to thank them when you're done!