Either you think you're REALLY REALLY valuable which I suspect is your problem, or you have other things of importance in your life like family. Some old people have NOTHING but their animal companion, nothing else to live for. No, you don't SOUND heartless, YOU ARE, if you have no empathy for these old people.
Get a grip. Millions of animals die in the wild every day. We just don't know about them because they happen out of our sight.
Are you sorry for the rats who drowned? For the roaches that are now dead or homeless? Why are they less important than dogs and cats?
My sister's family has fled two hurricanes in the past year. They took their dog. They left their six horses to fend for themselves. When they came back, the horses were still there - a little hungry but otherwise unharmed.
Did they care about their horses less than their dog? No. I think they realized where they had to draw the line about what they could take with them in order to flee.
If you want to stay where there's no food, no water and no power for the sake of your pet, that's fine. Just don't whine about the mean old rescuers who won't let you tie up their resources for a dog when there are other humans who still need to be rescued.