I am trying to figure out if a long-term relationship is possible when one person wants children and the other doesn’t. My boyfriend and I have been together for four years, and we began to have discussions about the future recently, which ended with a chat about parenting. His views came as a surprise to me, which was also because we had never spoken about this before. He told me about wanting to be with me, and wanting to live together, but was adamant that becoming a parent was impossible because he had strong views that were non-negotiable. I love him a lot and want to be with him, but don’t know if I can change his mind going forward because it sounds like a gamble. What should I do?
You are both putting forth clear statements about your expectations, so making any decision based on the assumption that he will change is mind may not be a smart thing to do. He says it is non-negotiable, and your premise is that he may change his mind at some point. You should decide upon a relationship based on where things stand, and what has gone before, because we can’t predict the future. The information we have about a partner allows us to imagine a future with them. You can always hope, of course, but it makes more sense to evaluate how badly you want this relationship to work and what you are prepared to give up.

How do I end a relationship without both of us feeling like the experience has broken us? 
If something isn’t working and you want to end it, you can’t avoid the possibility that one or both of you may experience grief. What you can do is articulate what is and isn’t going well, and why you don’t see this working. That clarity may go some way towards helping your partner make sense of what is going on. Communication is always the best thing to avoid misunderstandings.