[setzf]

As a vegetarian and mathematician I find your friends offer and reasoning to be quite illogical. If he really wanted to adhere to his own reasons for not eating meat then he should want more people not eating meat and therefore him eating meat for a day instead of you gains nothing yet compromises his integrity.
So he is right that it is irrelevant who acctually consumes the meat but if he really believed what he said he would want nobody (or a significantly small portion of people) to be eating meat period. Not that he should be preaching to meat eaters but that he should encourage vegetarianism.
Sounds like he's a vegetarian just because it makes him feel good about himself.

PS of all the meats he could "trade" for he wants to eat turkey? i dont get that either.