Why are some people vegetarians and go around imposing the same?

Because they think it is more ethical practice to be a vegetarian, respecting rights of living and freedom of animals too. And there are some who believe in health benefits of being a vegetarian and choose to be one.

Regarding why they impose on others - not everyone does. Some just silently practice, some try to convince others to quit non-veg diet, only some do so intensely. Compare it with olden days when slavery was perfectly accepted thing - those who resist, why they did so coming out of their comfort zone and without being afraid of being sidelined? Because they believed it was right and wanted to uplift others around. Similarly, some vegetarians feel strongly that humans need to evolve further and be more compassionate.

Hope this helps.