The puppy, however, being dumb as a bucket of dirt, doesn't care, because there is no such thing as "caring" in animals. If it feels the pain of being kicked, it will instinctively do something (probably bite me). If it feels me petting him, it will do something else. It's mindless and automatic. Animals are sentient, but they aren't rational beings. That's an important difference.
I'm aware of that difference. That's why the argument is focused on animal sentience, not rationality. The 'dumb as a bucket' puppy may not be rational, but it is sentient. I'm not going to tackle whether its motor functions and sentience is a product of mechanical automation. I don't believe it is. Anyway, a big factor is whether or not we should do good to one another. Unnecessary pain is bad. A dentist may hurt you when drilling your teeth, but if s/he didn't, you would be in greater pain later. So the pain is done to avoid greater, unnecessary, and preventable (<=I may be redundant here, so ignore this if I am) pain.

A drowning puppy should be saved, whether drowning by itself or drowning next to a drowning Nobel Prize winning individual. The difference is that in the moral question regarding a puppy and a baby is that a baby is potentially more practical than a puppy. If a puppy was drowning by itself would you not try to save it? Simply speaking the answer is yes (I could go into things like saving random animals that fall in water, especially when they are overpopulated, or something).

Anyway, the basis for treating puppies well is because they are sentient and feel pain. Also, whether or not we deserve to be treated well (goodly), we do it to each other (or try to), and should do in kind to animals. I'm not advocating veganism, which would still result in the killing of field animals when the giant tractors run them over, but that we should have consideration for them. Senseless slaughter of animals because 'they aren't thinking things' is irrational, unless you can prove to me that animals don't feel pain when you take a scalpel and cut them up, or do live autopsies like our favourite philosopher/scientist Aristotle (or so I've heard. If he didn't somebody else did throughout history, and you can substitute his name there).