So you obviously finds your wife's views on this unreasonable; do you normally find her to be a reasonable person?
My guess would be yes, otherwise you wouldn't have married her, but for all I know you could be a sadist or something. (aren't most people that ger married... j/k, kind of)
Anyhow, if your wife is normally swayed by reason, I think a patient persistence might be in order here. You obviously can't expect to change her mind about beliefs she's had her entire life in a few conversations, but if you keeping chipping away for awhile, you may find that she eventually comes around.
I actually find the fact that she's starting to have trouble talking about it promising. If she was firmly 100% set in her beliefs, she might very well have no trouble at all talking about it, but the fact that it upsets her may very well show that she isn't so secure in her beliefs, and is going through a difficult evaluation process in her mind. Even though she may not always be responsive during the conversations you guys have on this topic, I'm sure she has lingering thoughts about them well after the conversations are over.
So my advice is to be patient and persistant, and love her in spite of the flaws you perceive her as having, as that is what you would want her to do for you.
Best of luck.