Are you achieving your own goals or someone else's? If you want to achieve something to prove others, possibly you are just working on what they want, not what you want for yourself.
When people get challenged by others, they take it as their ego and pride. They want to prove others wrong so they try put their efforts and hard work to have a sense of achievement by not accomplishing their goals but by showing others that they can do it.
When anyone works with such an attitude, they get distracted from their real goals. They forget that the true meaning of success is not to display their abilities to anyone but themselves. Even after that achievement, one doesn't feel successful because learning and growth only happens when you focus on yourself, not by showcasing yourself.
No matter how much anyone doubts you, put your efforts into what you want in life. You just need to prove your abilities to yourself but no one else.