But back to women. I just don't see the point in locking eyes with women in public. Most of the time, it makes women feel uncomfortable, especially if they do not find you attractive. I suppose if you are into casual encounters, making eye contact with women may lead to something. But even then the chance of that happening is extremely slim. Most women will just think you are a “creepy” man.
That is more continuous staring (assuming t's not an obviously mutual thing). Can't think of any friends getting upset because a guy made eye contact with them, but it's just plain weird and disconcerting when you have someone unilaterally staring at you for a significant stretch of time.
For me, making eye contact in public is not really something I do unless I am engaging with a person. If, for example, I am walking on the street and people are walking past me in the opposite direction, I don't look them in the eyes, I look around them. Of course, if a person were to stop me and ask me something, then I'd have no problem making and maintaining eye contact.
Based on what I've heard from other women and from lurking over the years on forums with majority female userbases, most women tend to feel uncomfortable, self conscious, etc. when a man is looking at them (either repeatedly or staring) in public. A fleeting glance is fine, emphasis on fleeting.
But yes personally I avoid it when I can. I don't see the point of making eye contact with random women in public. The more attractive a woman is, the more likely she is already in some kind of relationship. So for me it makes the desire to make eye contact with such women even more bizarre.
I also live in England and the English, and Brits in general, tend to have a more reserved attitude towards eye contact in public (it carries a negative association), so there is that cultural influence, too.
I hear in other parts of Europe, it is more socially acceptable to stare and look at people.