To answer your question a pet should be rehomed any time a person wants to. Why? because if they want to re home the dog and are convinced to keep it, they aren't going to give it a good home.
However, if a pet is rehomed for a stupid reason, then I think the person needs to think long and hard about getting any other animals in their life. Pets are not disposable things that can be bought and then given away whenever you please.
Moving, having a baby, peeing on the carpet, and most of the other reasons you see on craigslist are not good reasons in my opinion. You may have to look harder but you can always find a place that takes pets, even if it is more costly. If you are going to rehome a pet the second you get pregnant you shouldnt get a pet. Give the dog a chance, they may end up being wonderful with your baby. Dog pees on the carpet? chews carpet? ruins your laptop & hot rollers (thanks Armani!)? TRAIN them, hire a professional if you can't do it yourself. I also hate when people say they don't have enough time for their pets- before they get pets they need to realize they require feeding, walking, grooming, etc. You can even hire people to help- there are people who walk dogs and even run with dogs for a living.
However, if someone like this lady on craigslist can physically no longer care for their pet- that is sad and might be in the pets best interest to be rehomed. I wish someone in this ladies life could take care of her pet for her because having the dog with her would probably be good for her mental wellbeing.
So anyway- a lot of rambling to say- most, but not all, of the reasons people get rid of their pets for are excuses and nothing more- but I still think the dogs are better off rehomed because
no pet should live in a place where they are unwanted and plenty of yorkies on this site prove how lucky a rehomed yorkie can have it. 