The numbers in the paragraph refer to further explanation below the paragraph.
Another kind of pet is the caged one. There are three main kinds of caged animals: birds, reptiles,(1) and rodents. Because they are colorful and graceful to look at, birds are very popular. In my country, some people have only one big bird in a cage, but others have several small ones,(2) fluttering and chirping around,(2) in a single cage. I would never consider having a reptile,(3) such as a snake,(3) in my house, but a friend of mine has a boa constrictor in a cage in his bedroom. He says that it is a lovely pet, since it doesn't bark, doesn't eat much, and never needs to be taken out for a walk. Rodents are small, furry, cute animals like guinea pigs, gerbils,(1) and hamsters. They are especially popular with children. If they are treated properly, they can live quite a long time in their cages. Caged animals have a fascination for people who mostly like to watch their pets.
(1) Many publishers will eschew the comma before the last item IF no confusion will result.
(2) This is related to the rule for the wh- relative clause. If we didn't use commas the phrase "fluttering and chirping around" would be a modifier used to distinguish fluttering and chirping "small ones" from small ones that don't flutter and chirp. Here, "fluttering and chirping" isn't an identifying trait that distinguishes certain "small ones" from other "small ones"; it is only extra elaboration.
(3) This is similar to (2). If he used commas, he would be saying that he rejected only reptiles that are like snakes but would accept reptiles that aren't like snakes. This reader thinks that the writer means he doesn't want any kind of reptile at all, and he's using 'snake' only as an elaborating example.