I actually think it is a nice tradition, especially since it is just ceremonial and has no substantive meaning. It is more a show of respect by the groom-to-be. It is an extension of the father walking the bride down the aisle and the minister asking "Who gives this woman...?" I happen to like that stuff. Goes with men opening doors and taking the curb, etc. If a man is gracious enough to do it and there is no submission implied, what it the harm?
Mostly what PEllen said. The harm that I see is that it reinforces (even if only on a subconscious level) the idea of women as property. "who gives this woman?" No one because no one owns her. I mean if you like it, ok, not gonna try and tell you (or anyone) not to go for it.*I* object to it as a concept, and definitely for me.
Opening doors, etc.? That's just manners. Yeah it's all cool when a guy does that, and I let them, but because I'm not threatened if some man does that for me, in a date/romantic situation or just a stranger at the bank. Then again, I do it for other people, men and women all the time just because I think it's polite.