There are many reasons why cats like to have their bellies rubbed, but one possible reason is that this behavior makes them feel comfortable and relaxed. Cats' bellies are a weak point on their bodies, so if they feel safe and trusted, they may be happy to let you pet their bellies.
In addition, cats will make a "hmm" sound when touching their bellies, which is one of their ways of expressing pleasure. Cats may also stretch when their bellies are touched, possibly as a response to the feeling of comfort. Finally, cats may also like to have their bellies touched because they find it a form of intimate interaction. The bond between cats and humans can be established and strengthened through physical contact, so they may find having their belly rubbed as a pleasurable way to establish and strengthen their bond with you.
