Basically, the reason (some) men don't want a vasectomy, is because they see it as an invasion of, and an insult to their 'manhood' and their masculinity. 'Snipping my semen tubes? Fuck off!'
And don't anyone say men don't/won't think this way, because they fucking do!
It's more painful and invasive having a root canal, or a filling, but no man will refuse this, because it doesn't involve his bollocks.
Most men (and some women it seems!) are happy for women to be poked and prodded and cut and invaded up their vagina though.
Well..... it's only da wimminz innit? It's just their lot in life eh? 
@MayYouLiveInInterestingTimes
Cokie3 that is too harsh, women do not have good choices in sexist Britain. It's entirely possible that a man will walk out if he is faced with the choice of having the operation for a woman or no sex.
If my man had said he will leave ME if I don't get myself sterilised, I would have packed his fucking suitcases for him, kicked him and all his shit out the front door, and changed the locks before he could get a word out.
Then again, my DH is not a spiteful, self-centred cunt, who would have left me for refusing to get sterilised. As cokie said, any woman is better off without a man like that anyway. And if he thinks any other woman he shacks up with, will be happy to have her insides cut into, to appease HIM, he will be in for a shock! Most sensible women will tell him to fuck off...!