I kind of agree with her. I mean, if you simply don't eat red meat then you're doing so for health reason and not moral reasons (since if it was the killing animals thing, you'd be a vegetarian), so why shouldn't you be able to simply handle red meat?
I mean, simply not liking a job ("it smelled so bad"), doesn't mean you should be excused from it.
I'd understand if you were a vegetarian/vegan and were against eating meat in general because of the animal-rights issue, but...you not eating red-meat is more of a food preference than a stand on anything. You can't expect people to cater to that.