Some people are concerned with invasive species destroying wildlife, and to a degree rightfully so.

Some people think reptiles are icky and don't want neighbors having any, especially large snakes.

Some people think owning pets is morally wrong.

They are all behind this bill, but the bill's proponents market it towards the environmentalist crowd because
1) it's the biggest group
2) people in the "reptiles are icky" crowd don't need to be advertised to to get their support for banning certain animals as pets
3) the third group knows they are unpopular so try to stay in the shadows to get their agenda passed as law

Regardless, if this law passes it will do nothing to stop the problem with burms in the everglades, snakeheads in the potomac, or asian(silver) carp in the midwest. These are the species that this entire bill is piggy-backing on. There are other invasive species out there, but only the burmese python has ever regularly been kept in captivity. The dozens of other non-native plant and animal species that have established themselves in the US were intentionally(or unintentionally) introduced into the wild without ever making it as popular pets.