I often talk to people about how, for this very reason, when it comes to ending long-term relationships we should expect to break up multiple times. As seductive as it can be to think we can just break up and move on, it's also normal to find ourselves wanting to reach out to the person we've just ended things with when we're upset - even when they are the cause of the upset.
The problem with this kind of reaching out is it can slow down or, in some cases, block the learning process that needs to take place to "move on."
It's also true that if you find yourself getting stuck it can be useful to intentionally generate anger, or feelings of not liking and annoyance, to help shift that attachment programming. It might sound a bit brutal, to deliberately focus on the things you don't like about someone, but it helps untangle the love and intimacy etched into our neuronal circuits.
And a lot of the time, breaking up is aided by, or requires, distance. Most of the time the distance, anger and focusing on not liking happens naturally; it's part of the grief cycle, but getting stuck can require us to create distance - to cut the person off, even if only for a while, to grieve effectively.
If your ex-partner doesn't require that, then good for them. It may be that their attachment system moves on quicker, that for whatever reason they don't get as stuck. But it's vital you listen to what you need, and are able to reflect on what will work for you - because getting stuck in a cycle of bouncing back and forth from a connection with an ex - even if no sex or physical intimacy occurs - can be quite destructive and really block the natural grief process.
So feel free to generate anger, be clear that right now you need distance and can't be friends, and focus on finding others to talk to when you're upset, even if you notice urges to reach out to your ex. Give your feelings, and your grief, the time it needs.
One day friendship might be on the cards; it is entirely possible to be friends with people we've been in relationships with. However, it's certainly not required, nor is it a marker of being "over" someone. It certainly doesn't mean there's anything wrong with you if you can't.
Some people just love deeply, and that can mean that seeing people we've loved and lost, always hurts.