Sorry. Yes it might be a pet, but I still thing its a very unreasonable thing to complain about and I still think that whilst a child is superior to a pet, a pet is still part of family life and unless that animal is actually breaking the law in some way, you have to respect that.
When you take on an animal you take it on for life, and take that responsibility. You can not just rehome it because your neighbour doesn't like the way it behaves. Its a living being, and like a small child there a some instances where you really can't control the way it behaves because you can not communicate the problem to them. Its not the animal's fault and in many cases, it probably isn't the owners fault either.
What really irks me, is that there is also a double standard when it comes to what type of animal it is. The idea that its ok to even suggest rehoming as if the animal is a throw away item is appalling. There is no evidence whatsoever about ill treatment.
Plus there is a real double standard when it comes to pets. Some pets are considered 'worthy' and part of the family whilst others are not.
If I put up a thread about a cat shitting in my garden and someone suggested my neighbours rehome their cat because it shits all over my garden, I can imagine the reaction. It'd get short shrift by a hell of a lot of people, as its considered natural behaviour and not a nuisance (they could keep their animal in their premises but thats considered cruel in the UK despite it being law in other parts of the world). And yeah I might have real concerns for the SAFETY of my child using my own garden because of the behaviour of their animal. In this particular situation though, you are not talking about safety - you are only talking about an irritation that the OP WILL get used to in time.
When people live under flight paths of major airports and they cope with that with small children, I really do struggle with this. Noise and coping with noise is a part of life. Animals are part of family set ups. They aren't children, but you know what that doesn't make them something that can be tossed out with the rubbish or something that you don't have to put up with from your neighbours even if you don't like them. You do.
Unless that animal is being mistreated, or breaks you have to just deal with it.