Ok, so here is the thing.
You are weird!
By very definition, because you are making choices counter to your culture and the culture of those around you, you are weird, and you should be aware of that. There is nothing wrong with that, but you can't expect others to know that your weird and not want to learn more. It's human nature. Your different so lets talk about how your different.
So as humans we try to do two very different things. First we try to explore and understand what makes us different. Second we try to make everyone uniform and the same. It's really odd that we would try to do both at the same time, but we do. What can I say, well all a bunch of wack-a-dos.
The Exploring Questions
Now, from your post you don't have a problem with the first part. People trying to question and "explore" your reasons. That's good, because while it's annoying (to you) it's also the only way anyone is ever going to understand you, and understanding is the only way your going to be able to participate in a community.
The only advice I will give there is try extra hard to answer those "explore" questions honestly, but without judgement. Suggest that I am less then you because I like my moo cow, and well, then your opinion just became lower then dirt to me. But if we have a conversion where I ask you "So why don't you eat steak?" and you respond with an answer that is honest and not aimed at making other less then you, and all of the sudden I may have learned something, at the very least I will make sure to have salad stuff when I invite you over for dinner.
This is easy, just use your I feel statements. And answer with your honest opinion. "I feel that eating beef is unhealthy," is much better then "Eating beef is unhealthy." Just be honest, non-judgmental, accept that your different and that people are going to ask, and your good.
The Conformity Questions
These are the bad ones. Well there not too bad, but they are the questions where people try to convince you that your way is wrong and there way is right. A lot of times, this is the "second" question.
For example "Why don't you want a steak?" "I feel that eating beef is unhealthy." "Well, do you have any data to back that up?"
Now the real trick with these questions is that you need to be open to them. If you don't eat meat, and you know why, then it doesn't really mater, unless your reason is invalidated. You should always re-evaluate every stance. That's how you grow. But while you may want to re-evaluate, the point is, that your not ready now to conform to the "normal" practice of eating cow.
I suggest a two step approach. First, re-state your I feel answer. Then if that doesn't work, leave. Honestly, it's fine for people to try to convince you. But if someone is going to ignore your feelings and beleifes then there not worth talking to anyway.
I'm not talking about a conversation where your willing to talk about your way of doing things. That's different and your agreeing to have, and participate in that. I am talking about the conversation where your just trying to eat your lunch and someone keeps pushing.
For example. "Why don't you want a steak?" "I feel that eating beef is unhealthy." "Well, do you have any data to back that up?" "Not really, but I still feel like eating beef is unhealthy." "Yeah but without any data, how do you know. One sirloin isn't gonna kill ya and you might like it." "I hear you but it's not something I want. Like I said, I feel I am making a healthier choice." "Come on just try a little one, there really good here." -- This is when you just leave.
Your a weirdo, get used to. Others will want to ask about it, but expect others to respect your feelings, and try not to come off judgmental your self. It all else fails, just walk away.