There are many reasons to not eat meat, but if one of yours is that you are 'compassionate', or love and respect animals, then you really should consider not using mass-production milk and egg products. Even if those aren't your reasons, milk and eggs really aren't the healthiest of things, regardless of what the clever advertising would have you believe!
It's usually a little inconvenient when you're eating out, but at home it's a lot easier because you can control what you eat and there are many alternatives. It's worth it though, believe me.