You don't have to argue with them about "how long" you will be a vegetarian.
If they say stuff like "That won't last" to you, just say,
"Well, TODAY I am not eating meat."
And then, in a few years, when you are still a vegetarian, they will realize that they were wrong and that you did, indeed, stick with it.
As far as people offering you meat - get used to it. Some people will be offering you meat even if you have been a vegetarian your whole life. Seriously. That's just how people are.