As far as why describing Mars as Earth's backup plan rubs people the wrong way, I think it's a bit like Noah's Ark. While there is absolutely the cute story about the boat full of animals, and it does make for a good story, there's also the "meanwhile literally everyone aside from a minuscule elect ends up dying" bit. Which would be nothing but sour grapes if you didn't see people holding up the possibility of colonizing other planets as a mitigating factor that implies that we really shouldn't be quite so worried about all the environmental damage that's happening here on Earth. But you do.
Put it all together, and the complete narrative starts to sound like, "Sure, we're recklessly hurtling toward turning the planet into an inhospitable shithole for billions of people, but don't worry about that, because 0.00000005% of them are going to get to live on a completely different inhospitable shithole instead!"
Which, disclaimer, I'm not wanting to pan human space exploration. But I much prefer the "exploration for the sake of adventure and discovery" narrative. If that's not good enough, the ground to retreat to should be robots, not messianic fables for rich people.