Rest in peace

How come we put our dogs and cats to sleep when they become old, sick, in pain, and begin to pee on themselves, but when human beings becomes old, sick, in pain and begin to pee on themselves we make them stay alive to suffer through it?
To me, it seems we are more humane to the dogs and cats. We don't want our beloved pets to suffer, so we do the right thing and put them to sleep. Does this mean we care more about being humane to our animals than we do human beings?

jb