Why don't birds get electrocuted on power lines?
Because electricity needs a path to somewhere at a different voltage, and a bird sitting on a single wire does not provide one.
The principle. Current flows in response to a potential difference — a voltage gap between two points. A bird with both feet on the same conductor has both feet at essentially the same voltage. There is no difference across its body, so no meaningful current flows.
A tiny current does pass through the bird, because its feet are a few centimetres apart on a wire with some resistance, creating a minuscule voltage difference. But the bird's body has vastly higher resistance than the copper or aluminium beside it, so current takes the wire — the path of least resistance — and what passes through the bird is negligible.
Being "live" is not the danger. The bird is at 11,000 volts, or whatever the line carries. That is harmless in itself; it is only dangerous relative to something else.
When birds do get electrocuted:
Touching two conductors at once. A large bird with a wide wingspan — herons, storks, raptors, owls — can bridge two phases, or a phase and a neutral. This is why bird deaths on power infrastructure disproportionately affect large species.
Touching a wire and a grounded structure simultaneously, such as a pylon, transformer casing or pole. This is the more common cause, and it is why utilities fit perch guards, insulating covers and elevated perches on transformers.
Wet weather reduces the insulation of feathers and increases risk.
The same principle applies to people. A person in an insulated bucket touching only a live line is not harmed — which is how live-line maintenance is done. The danger is providing a path to earth, which anyone standing on the ground does.
Never assume a fallen line is dead. Ground itself carries a voltage gradient near a downed conductor, and taking a normal stride can create a lethal difference between your feet.