You shouldn't give people nosebleeds.
Nelson was annoyed by the other kids in school mocking them.
Nelson wanted to make the other kids stop mocking him.
Nelson simply decides to ignore the mocking kids completely and pay no attention at all.
Nelson punches the mockers in the nose and gives then nosebleeds.
Eventually they stop mocking Nelson when they find something new to mock.
Sure enough they stop mocking him out of fear of another punch.