Do you think it's okay that I try to act manly in front of my dad?
I'm not sure. Why do you try to act manly in front of your dad?
I just want to be equal with him no matter how unsuccessful I am
There's no reason to pretend to be macho to try to impress your dad. You should be yourself, and not try to act differently to please other people.
But I don't know how else to get my dad's approval.
I'm sure if you're a good person and do your best your dad will approve of you. Acting like a tough guy to please your dad, or anyone else, isn't the right thing to do.