How do you know plants don't feel pain?
There are several points to make here, but the most important one is that eating meat "kills" more plants than eating plants, simply because you have to feed plants to the animals you eat in the first place (and it's less efficient than eating plants right away, it's that simple).
Apart from that, it's just a matter of varying degrees of certainty. Am I "sure" that other humans apart from me feel pain? Well, pretty much so - you can never "prove" such a thing, but pragmatically speaking, yes I'm sure. Am I sure that other mammals feel pain? It's at least very likely, because they are evolutionary, anatomically and behaviourally so close to us. I study neuroscience/AI btw, and I can tell you that the brains of other mammals are essentially the same as ours.
Now, the further I go away from mammals (fish? Insect?), the more difficult it is to say. But that I cannot fully exclude that, say, a stone has feelings shouldn't keep me from trying to avoid causing pain to higher animals where I can be almost sure that it is the case.
And with plants, it is rather unlikely that they feel pain. First, they don't have nervous systems like us. More importantly, developing pain perception just doesn't make sense evolutionary for plants, because the point of pain is to make an organism rapidly avoid the source of the pain, and, well, plants can't move, you know (with very few exceptions).
Even if organisms do have some reflex-based avoidance behaviour, it doesn't mean that they consciously feel pain. But yeah, this is a very very difficult topic. But again, the fact that there exist grey areas shouldn't make me ignore the (almost) white areas.
It is, especially since more and more people are turning into vegas. Personally I think that vegetarianism is the is the biggest bullshit ever. People would like to believe in this, they think that it's good for their health.
As has been pointed out, many people do it for ethical/ecological reasons. Personally, I can see why people say "I just like meat too much", but I feel offended if people question or even ridicule the reasoning behind vegetarianism. I value my rationality very high.
Oh, and with Gandhi, Hitler, Einstein and Christian Bale on my side, I have to be right, right?