Who wears the trousers in your relationship?

My girlfriend doesn't want to admit it that even though I'm petite and short where as she's very tall and athletic I am still stronger than her. But the problem is, she tries to keep it secret and doesn't want people to know I can beat her in an arm wrestle and i can carry her longer than she can carry me. I feel like she is ashamed? I want her to stop patronizing and undermining me, I want her to stop pretending she's the physically dominant one when she's not, she is lying so I want to prove her wrong infront of her friends but I don't want to hurt her at the same time, what shall I do?