Due to the lack of neutering and spaying, more animals are populating the streets.
As more animals populate the streets, more animals are brought into shelters. Shelters are filling up and running out of room for every animal. Animal shelters are forced to put down older and sicker animals.
For every animal that is spayed or neutered, the number of wild animals in the streets goes down. When the number of animals on the streets goes down, the shelters fill up slower. With fewer animals in shelters, there are more animals in loving homes.