A lot of animals at animal shelters across the world are left behind by their owners because of moving. I think it's sad when the owners can't place their pet into a decent home and have to choose either the shelters or the street for their once loved pet. Certainly, you don't really hear about parents leaving their kids behind because when a family moves to a new location. Of course, kids and animals are different. But one must demonstrate similar commitment. After all, you are caring after a living being.
After 7 months in our house, I think the "new" cat Lola is finally getting comfortable around us, and our Elphie. The two cats were once sworn enemies, but now they play together, sleep together, and get on each one's nerve as well. It took a while to get this peaceful, and we got lucky because we had to move from an apartment to a house so that these two cats won't fight as much (and the house was no one's territory, where as the apartment was Elphie's). Now, Elphie, as the younger cat, actually becomes submissive to Lola, who is 3 years older.
Shelter life is not good for any animal, it's like living in minimum security jail but with the possibility of the death sentence. Living on the street is not good either since life expectancy drops significantly (and who knows how grisly the death would be...).
In a way, having a relationship with a pet is harder than having a relationship with another human being, in the sense that you can't just break it up if you don't like it. I suppose the consequences are not as severe even if you do, thus explaining the countless of homeless animals out there, seeking for housing and affection, and possibly a life of never having to move again.