There have been some really informational posts on here (thanks, ladies) but I thought I'd throw my two cents in anyway.
BJCM - you could have IBS (Irritable Bowel Syndrome, aka Spastic Colon) which is triggered by certain foods. Or you could just have a sensitivity to red meat? You can have an IBS attack because you eat a certain food, or if you're stressed out, or for many reasons. Two big triggers for me are red meat and stress. I get upset, and it goes right to my stomach. Go figure.
Side note: the first time I met FH's family - stressed out, of course, and they had steaks on the grill. I was in so much pain!
But I digress. One thing that works for me (because I do love a good steak) is moderation. I don't eat much red meat because frankly, I don't enjoy spending my evening on the toilet. But I've found that I can enjoy it occasionally with no problems.
Do what works for you - and tell FH you can get the vitamins you need in many other places. Maybe he's just worried that if you change your diet he won't get some of the yummies he's used to? 
Good Luck!