Should I study Catholic doctrines so I can win in debates with my Catholic friend?

What a waste of an excellent learning opportunity. Go ahead. Learn what you want for what reasons you want. I'm sorry to see you'd be wasting all your time and energy, and life, in studying for something so great as the Roman Catholic faith, just to win "a little debate" or two with your friend. Life always seemed so much more important to me. God Bless you.