Why do people look for rebound uncommitted relationships, and tell their previous relationship that they want them back and that they are the only one that they love?

Chemicals. It is unfortunately the case that our biology dictates much of this. When you are with someone for a long time, you become mentally and physiologically used to having them around. The trope of "leaving a hole" when you break up with someone is very much a real thing. Hormones and neural connections that your brain and body expect (including the feeling of waking up next to someone, the urge to speak with them when you're upset, etc.) are suddenly denied, and it is a bit of a shock to the system. People try to fill that void with meaningless rebounds because they think the change and thrill will substitute for those chemical responses, but they rarely do.

Sometimes people think that these physical relationships or flings will make them feel better and all they can think about is feeling better but then after come to a realization that it didn't help and begin to think about the person they truly have feelings for. They sometimes fall into a cycle of it though

As cliche as this is, the heart is fickle. For some people, it takes a change, for example a rebound, to appreciate what they lost. They need to experience what they don't want to understand what it is that they do want.

Often times people become afraid of being alone when they break up with a significant other. They become afraid of moving on to another committed relationship in fear that they may never find one. Because of this they often have rebound uncommitted relationships to try and quell that fear as well as tell their previous relationship that they want them back out of fear that they may never find someone else. They use their previous relationship as a back-up plan to fall back to if they find they have no success moving forward.

After a comfortable long relationship a sudden breakup leaves you shocked, unbelievably lonely and ego wounded, rebound may seem a revengeful solution only to make more miserable and wanting your ex back, so that you can either get back at them or with them.

We look for rebounds in order to try to get over the hurt we have from a past relationship. Or we might do it in revenge. We tell exes we want them back because we still have those feelings for them.

you only know what you have once its gone so that is why when soneone leaves and the realises that you were the best thing for them they will try and come back

Because the pain of separation is real and deep. And these are ways to cope with that separation. In my experience, the separation (if objectively needed and necessary) is an opportunity for growth and maturity. Sometimes, one may not feel ready for it. And so it may be difficult to take that leap.

People who look for rebounds often are feeling lonely and want that security of someone who is attracted to them. Perhaps it feels affirming. Maybe their trying to fill the void (left from their ex) as quickly as possible, not really caring who. And if they want the previous relationship back, it means they're probably comparing the rebound one to the old one.. and feel unsatisfied

Because as humans we truly don't know what we want. We get comfortable and when the intial rush of freedom is gone they find themselves sad alone. So they run to the comfort and safety of what they think must be there one true love. But is simple just a fear of change.