Unless you're a meat-eater who eats ONLY meat, i.e. meals consisting entirely of different bits of meat and nothing else, all the time, it won't be a big deal to go to a dinner party or veggie restaurant and not have meat for ONE meal, unless you're a whinging whiney pillock who insists on making it into a big deal.
A lot of non-meat-eaters will avoid meat for various kinds of ideological reasons, sometimes religious, sometimes health-related. Some of those reasons may make it objectionable for them to handle and prepare meat for others, whereas it's unlikely meat-eaters will have the same kinds of objections to preparing vegetables for non-meaties, beyond the "pain the arse" factor mentioned above.
It's one of those issues that needn't be an issue. It becomes one partly through some vegetarians, as has been said, being pious and preachy about it; but it has to be said it's also partly down to some easily-baited meat-eaters bristling a little too readily at any mention of vegetarianism, suggesting they're a tad over-sensitive about their eating habits, for some reason.