This one I disagree. There is a time to show a woman attention and care but a professional environment is not one of them. In a professional environment everybody is equal, you are there for your skill set. Why should ones being a woman entitle her to any different treatment? If I am out to dinner with a group of friends in a social situation and I choose to pay for a female friend all the females then so be it, but at work no woman should be expecting, or taking meals for being a woman. It lowers her value to do so.

Your scarf example is entirely different. If a man walked by and dropped his scarf, and I was closer to it, i'd instinctively grab it for him as i would for an old lady or a beautiful young woman. There is no special treatment, there is no sexual context. Just a kind gesture. In the case of her dinner, specialized treatment.