He is providing a counter example, which is not the same as generalising.
It's not really supported by the anecdata that OP is a skilled, unsociable, successful person. That only tells us that this person, in their particular line of work, with their particular set of skills, can be successful. It also doesn't consider whether a version of them that was more sociable would be more successful.
Given parent is an introvert and succesful the statement is true.
The maximum success of extroverts or the average or the mean?
What exactly is meant by succesful? What's the measure?
If they become more successful if they act against their self is questionable, like asking straight people to become a little more gay or vice versa.