Answer
The points at which the bird's legs come in contact with the wire have no or insignificantly little difference in potential. When there is no difference in potential, no current flows through the body, between the two points of contact.
Work Step by Step
Being electrocuted means that an electric current is flowing through the body, strong enough to cause tissue damage.
For an electric current to flow, a difference in potential is required.
If the bird had one leg on a high voltage point, and the other leg at a low voltage point, then due to the difference in potential (voltage), there would be a current and the bird could be electrocuted.
In reality, the two bird's legs are close together, touching the wire at points with almost the same potential (the same voltage), so no current, or rather an insignificant current flows through the circuit leg-body-other leg. No tissue is damaged. No electrocution takes place.
Furthermore, it helps that the claws with which the bird grasps the wire are not a good conductor of electric current, so the points of contact may not even close a circuit, even if there was a significant difference in potential.
