very very interesting subject....thanks for bringing it up
I don't like the whole lady's first thingy either....I want both genders to respect each other....I would keep the door held open for my guys' coworkers if they are just few steps away from the door and I reached the door earlier....but I get embarrassed if we are walking all together and I'm the only woman in the group, then they say lady's first....
however, between my guy friends, I'm okay with that....and we joke about it....
I think it all depends on the situation.....