Literally, the reason that Lennie likes these kinds of small animals is that he likes to pet them. In Chapter 1, that is what he talks about wanting to do. We also see this because his Aunt Clara gave him a rubber mouse he did not like it because it was no good to pet.
I think that figuratively, this is meant to show how childish Lennie is and how much he depends on George. He is so obsessed with little things that he can pet that he seems like a child.
