I really hope you have no pets because gods help them if you do.
Why? I would love it make sure it's properly feed, cared for and got it's medical needs met. But if a man comes to my door and says, "Sir we have to evacuate you right now [some disaster is going to occur] grab whatever you need and be ready in 15 minutes and, I'm sorry, due to space limitations we cannot allow pets."
I'd feel bad about it but I'd have to leave the pet behind I do not value his life more than I value my own.
I'm not likely to ever be in such a situation so if I had a pet I wouldn't have to worry about this happening. In a perfect situation, yeah, I'd bring the pet but if it's my life or the dog's, sorry, the dog's life is less important to me than my own.
All that means, however, is that you're willing to use your pet until it's no longer convenient to do so, and then you leave it behind to fend for itself. I'm sorry, but that pet is your responsibility. It is your job to protect it's life to the best of your ability. To leave it behind it unconscionable. It's not the pet's fault you can't plan ahead.
And if the best of my ability still leads me to a man standing at my door saying, "Sir we cannot bring pets along." I've done all I can. I don't think I'm in danger of any kind of situation coming along where I'd need to leave my hypothetical pet behind happening but if it were to happen -and I were to have a pet- I hope I'd first of all get out dodge before an evacuation would be required (and honestly no such situation short of an asteroid strike or war is likely to happen where I live). I'm assuming an unplanned, oh-shit, type situation here where the National Guard is coming by and going, "You need to get out, NOW! Godzilla is coming!" or something like that. A situation where time and space are critical and those forcing me aren't budging on the whole "bring the dog" thing.
Any pet I would have I would certainly love and done anything and everything for but I'm not going to value its life more than my own and if my survival mean its death then I'd probably feel very bad and torn-up about the loss. But I can't put his and my probable survival over my own ensured survival.
American laws, apparently, require evacuations to include pets, great and fantastic. And since local and national authorities are known for knowing all of the most recent changes to law and adhering to them and are in no way encouraged by superiors to only let it go into play when asked, I feel great about that. But since in the real world an official forcing you to leave your home isn't likely to be very accommodating when it comes to your "rights" and your pets it's still an argument you may lose. But that's all hypothetical.
I would try and save my [hpothetical] pet's life along with my own to the best of my ability but if the other party isn't budging on the issue or insisting I leave it behind in favor of my own life then, sorry, I'm going to go on living.
But we're talking about a likely never happen situation in my case as I don't live an area where a "your life or your pet's" situation is ever to come up. The most "disastrous" thing that can happen to me is a tornado and since I live in an apartment with no tornado shelter around me; him and I are pretty much both screwed so we can hide in the bathtub with a mattress over us together.