Answer: because they trust you sufficiently to rub their belly which they like.
This has been discussed before on PoC and countless times elsewhere but I want to briefly touch on it again.
This is really about cats doing something that they enjoy. They enjoy having their belly stroked but it does require trust. Some people argue that it is submissive behaviour. I have discussed that too. It is not about showing submissive behaviour towards us in my view. It is about pleasure, contentment, feeling secure and friendship.
For a cat to present their belly to us he has to be secure in our presence. It can happen just after a greeting. It is often a second phase after seeing your cat having been apart for a while. That’s the what my cat does.
When a cat is pleased to see you she’ll greet you and if you stroke or pet your cat she may roll over and present her belly to you. In this instance, it’s a second phase in the greeting/stroking process and a sign that your cat trusts you absolutely.
However, we all know that the belly is a well protected and sensitive area of the cat’s body so you have to be delicate in the way your pet your cat there.
My experience informs me, and many others, that you can overdo petting your cat’s belly. Go too far and your cat will be stimulated to play-fight. She may bite your hand in play. This is not true aggression. It is play.
Cat owners should be pleased if their cat wants a belly rub. I’d say that not all cats will do this. It is common but not universal.
I frequently pet my cat’s belly because he asks for it but I do it with great sensitivity. I also flea comb him there. Once again it is done gently but he likes it.
When you pet a cat’s belly you can see his/her demeanour change slightly. Cats become more alert to what you are doing so tread carefully.
That said, there must be some cats who are less sensitive about the belly rub and don’t mind if you are a bit rough. This is the personal part of the process. Each cat has preferences.