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Pigeons are actually known for being very agile, and are able to do vertical takeoffs and evasive maneuvers like a backflip loop immediately after takeoff, which is precisely to evade predators like falcons.

City pigeons just tend to become fat, lazy and used to suppressing their flee response around traffic and people.

Pigeons fly surprisingly fast and can outfly smaller raptors in a straight line. A stooping (diving) Peregrine will usually win. Its strike may decapitate the pigeon which tends to minimise the struggling

Except for the part where pigeon racing is an entire sport that relies on both their speed and intelligence

Except that it's not clear whether the intelligence† that underlies their homing ability is equally effective in helping them evade predators.

†Is "intelligence" even the right word here? I don't know. Much depends on how you define it, I guess, combined with the unknowability of the pigeon's own mental processes.