Not all breakups are created equally. The tone of a breakup is almost entirely dependent on the nature of the relationship that preceded it. That said, if you had a happy healthy relationship that was founded on friendship, you don't have to throw it all away once you and your partner call it quits.
It takes a considerable amount of maturity from both parties to come to a mutual agreement that ending the relationship is what's best for both of you - especially if you were able to do it without a third party mediator, screaming matches, or excessive pettiness. But if you're able to do that and decide to maintain a level cordiality or even friendship in place of a romantic relationship, just know that it's not weird.
People in our generation are quick to commend former couples for finding the civility to remain on speaking terms after a breakup, but can't seem to fathom the notion of remaining friends. "It's like a serial killer letting you go and then asking if you can keep in touch," is something I remember thinking after my own breakup. Why would anyone want to try and salvage a friendship out of a relationship that didn't work? Why not just forget it altogether?
My man -and future husband- Chris Evans really put things in perspective on the importance of staying friends with your exes in an interview he gave not long after he and his fiance split -putting me back in the running. He said "If you're ever fortunate enough to love someone and have them love you back, it's worth protecting that. It's rare that someone can truly know you. And if you've broken through that kind of wall, I think it's important to value that."
Breaking up is hard to do especially if one or both parties weren't ready to let go. If you're smart enough to recognize that you're not on the same page and that staying together will only hurt you both in the long run, you don't have to terminate your friendship along with your romantic attachment. If your ex can still be a positive and supportive voice in your corner, don't feel weird about allowing them to stay in your life.