Just a little friendly advice based off of my experiences.
How to Deal with a Break Up
We've all been hurt at some point in our lives by a person(s) who we thought cared about, or even loved, us. The thing you learn as time passes is this: loving someone and being in love truly are two separate entities. Loving someone is caring about them and enjoying/embracing their friendship to you--romantically, familial, or friendly. Being in love with someone is different, and it may not even happen to everyone, so when you find it, you'll recognize it, and should definitely cherish it.
I'm not a relationship expert of course but I've been hurt and have hurt people, sometimes intentionally and unintentionally. What I've learned is that you have to make decisions that best suit YOU and your life, future, etc. That unfortunately comes with hurting other people even if you try your best to avoid it. And once they've moved on, regardless of how long that takes, they'll usually understand. I know that's happened to me.
When someone you've hurt is angry, jealous, and/or stuck in the past, they often express themselves by utilizing hate. Whether that be verbal confrontation or passive aggressive comments, they want you to believe you haven't hurt them and they couldn't care less about what you're doing. They may even try to turn the comments around on you when you never said anything to begin with. But the fact is if they spare these random moments at all, it is clear to everyone that the pain still lingers. I've experienced this as well.
Although you may want to be their friend (or maybe you don't), they probably aren't ready. Time truly does heal all wounds even if that seems foolish at the time, and eventually they'll find another person or job or hobby that allows them to accept or come to terms with the past they shared with you. Sometimes this takes excruciatingly long, while sometimes it only takes a week or so. It solely depends on the aftermath of the breakup and how they chose to handle it.
The most difficult part is, in my opinion: refrain from retaliating. That's why they say and do the things they do. They see you're happy and have moved on and want to corrupt that even in the slightest way. The best (and only) "retaliation" is honesty ignoring it and moving past it, proving that--in time--the decision you made was indeed the best one for both of your futures. Sometimes you may never hear from your ex again, while other times you hear too much. This can be difficult because their comments may be straight up incorrect, or you may have the urge to just blurt out "grow up, move on, and stay out of my business." Don't. Eventually, they will.
And if you're the person mercilessly throwing unkind words out into the open about someone, reconsider, even simply because it makes you appear desperate and obsessive. If you truly have something to say to someone who hurt you, contact them directly. It couldn't hurt to try instead of reciting your issues to everyone besides the person(s) involved.
If you're attempting to move on but a person insists on acting childish and in turn doing or saying immature things, it only looks bad for them. Don't take it personally, they still hurt--and are possibly a bit jealous or bitter--and that leads to irrational decisions.
People fall in and out of love all the time, unfortunately. That doesn't mean a relationship was a waste of time--it helped shaped the person you are today. We learn by our experiences and our mistakes. You shouldn't pine over past mistakes and regrets. Embrace them and understand they can't be changed. Everything happens for a reason. The only thing you both can focus on now is improving your future by utilizing the amazing gift of the present. Focus on the positive and eventually the negative will weave its way out of your life.