Begging and pleading doesn't equate to love. Heck, someone can beg and plead for a relationship not to end for all kinds of reasons. Yes, love can be one of those reasons - but there are plenty of other reasons too.
My own view on why people fight for relationships not to end? It's because they don't understand that a good relationship needs two people who BOTH want to give it their all. If one needs to beg the other to stay, then it's all doomed anyway.
Never regret anything that has happened in your life. It cannot be changed, forgotten or undone. So, take it as a lesson learned and move on.