Girlfriend walks ahead of me, is she trying to claim the upper hand in the relationship?

I just noticed that whenever I'm walking with my girlfriend she always walks faster than me and ahead, especially if there is someone else with us walking. For example, if we get up to leave a restaurant or bar she always heads independently out the door, I don't chase to catch up with her because I want to show her that I am the one in charge, I walk at my own pace. I always open doors for her too, but she always just walks through and doesn't wait for me. Maybe she thinks I'm not an alpha male or something, which would surprise me as she was worried and uncertain if I would like her in the first place. I am good at seducing women and she knows that I could have other girls than her if I wanted to. Do any of you girls do this? Why? Would you not walk beside or ever so slightly behind your man?
Girlfriend walks ahead of me, is she trying to claim the upper hand in the relationship?
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