No one is going to yell, at you for somthing that you parents said and you asked what more you could you do?? I respect your mom, she has good points. I agree with some of her reasons. But I dont agree with-
She said they can learn to protect themselves like squirrels, birds, and other wild animals do.
I belive that What you tame is your own creation, you must care for it to bring it the best life. Wild cats and dogs can spread dieses, and things such as heartworm(my vet says). Which I was is a what we are trying to get rid of.

I talked to her about the population problem, and she said human children in many parts of the world are also homeless and dying. She said that does not mean humans should start spaying and nuetering their kids does it?
But people can fend for them selves without haveing to live rely something else. (example: Feral Cats have to dogde dogs, cars, mean people, ect)

*****Since your you only have a cat and a bunny, and they are inside pets, I do not belive that you have to get your pets spayed or neutered. Ive never even thought to get my bunnies neutered. The females are always seperated from the males.
My cats though Im alittle more worried about. My aunts cat got cancer from not being spayed and I would hate to lose Blueberry to the same fate, when she doesnt have too.

*********Plus some Women do get "Spayed" so to say.