I'm a man and I'll often try to walk women home if required, or more often nowadays a lift. The crucial element is to make the offer in as innoucous a fashion as possible, so this might involve making a general offer to everyone after a night out "anyone need a lift home?", but making that offer open to everyone.
My reasoning is if anything untoward happened to anyone in my orbit I'd feel terrible, so honestly it's as much about me as anything else. I am 6ft tall and reasonably well built so I don't usually cop any flak when I'm out and about, and whilst I did get stabbed once (and I got very lucky in that I got only a very minor injury) as a teenager although I avoid violence at every opportunity I'm not particularly phased by it.
However, and I think this point is crucial the sort of people who go rushing into potentially dangerous situations to help other people are uncommon, and gender is by no means a predictor. I think we do women a disservice here as evidenced by this study here:
www.ncbi.nlm.nih.gov/m/pubmed/15222859/
What this 2004 study indicates that in lots of occasions women may actually be more brave than men are, but men are more likely to get medals or recognition for such behaviour. I think this is an important point as I think this men need to protect women narrative is inaccurate as I think women do a lot more protecting of themselves and others than they are given credit for.
I've known a fair few women who are perfectly capable. On one occasion I rushed out onto a street upon hearing a woman's scream. A man was was attacking her and she was in the process of effectively fighting him off by whacking him with her umbrella. I'm not sure I made a massive difference to that episode, besides giving him a little extra incentive to run off.
I won't be encouraging my little boy to think in terms of having to protect women. However I will be raising him to know there are violent people, more usually they will be men, and there is everyone else. People in the everyone else category need to work together to keep one another safe and the gender in that group is irrelevant. This framing that women need to come to us for protection is innacurate and wrong.