Next time they ask if you want meat, just say no thanks. If they ask why, just tell them that you don't really like that. If you are too nervous to do that, just make sure to know when they're making meat for dinner or whatever, and fill yourself up before it. Then eat anything else in the meal (particularly anything like salad, super-healthy stuff) then be like "Man, I'm full!"
Spend a few sleepless nights worrying about it. Write one or 2 pages about it in your diary. Think, worry, and whisper about it for a month. Go through a near death experience and finally decide you can't hold onto this dark secret any longer. Give a long-winded, emotional speech. there, secret's out.