It is clearer to fight the battle that a significant number of men are a danger to women.
I am not so sure. Men know that they are a danger to women. The men who oppose the women only taxis want to continue being a danger to women.
There is, from my point of view, no need to repeat this point as the reason why there need to be women-only things but not men-only things.
Men already know that.
It is better to allow them their men only taxi service so they cannot oppose the women's taxi service anymore than to risk that women have no safe option to get home.
What do you mean by The problem with the men only would be if the area was of a male dominated employment.?
If something is male dominated from the get go, then implementing something exclusively for women will enable more women to do that job as they won't be harrassed.
Men going on to found their own "men only" thing won't matter, because in fact, the thing was men only beforehand, too, it just wasn't official.
It would be a bit more of a problem for things you study at university, but if there was a women-only university for physics or engineering and stuff, I think many women would prefer it to others. One or two other universities declaring that they'll go men only won't affect them much.
(And many male students wouldn't want to go to a men-only university as they wouldn't meet women there ...)
Also, I don't think all men would go join the men's only taxi service; most would realize that it would be idiotic to limit their customer base to the 50% of people who are more likely to be violent towards them.
Men are not discriminated against because of their sex, and I think allowing them to found a men-only thing and let them see that absolutely nothing has changed for the better, might help them realize this. (Of course, they do not really want a men-only thing, they want to have access to women to rape, but they won't dare say that aloud. So, give them permission to do something for men only, and see what happens.)