Some parrots can have very long lifespans. Like if you wait until you're 30 to get one, your bird might outlive you.

Being able to fly greatly reduces the amount of predators that can eat you (as does being big, like elephants or whales, being generally out of sight and looking inedible, like naked mole rats, or being a walking extinction event that eradicates any predator stupid enough to mess with them, like humans, as long as we aren't alone).

Most animals, especially small ones, generally will get eaten long before senescence becomes a problem, so they have no evolutionary pressure to select longer lived individuals.

Flying small animals, however, can escape predation often enough that that enough individuals die of natural causes that longer lived ones might have a sufficiently better chance of passing on their genes to be significant from an evolutionary standpoint.

So that's probably why larger animals tend to live longer, and birds and bats (and naked mole rats and humans) live much longer than other animals of the same size. (Bats have similar lifespans to birds, some reaching 30 years.)

Wild albatross can live into their 70s

I guess Ol’ Windbag Winnie was a smoker then, with such accelerated aging.

Pretty much this. The average gets dragged down by a HIGH infant mortality rate - nest predators from snakes to raccoons to hawks and vultures kill a lot of hatchlings, as well as things like simple accidents (falling out of a tree, for instance).