Withers can harm them self and other Withers with the explosion created by the impact of a Wither Skull. This causes a Wither to severely damage it self or other Withers over time. The Wither Skull itself cannot harm a Wither.
Steps to Reproduce:
1. Make a new Creative world.
2. Spawn a Wither. Make sure there are no mobs in the area.
3. Once it has spawned, spawn an Iron Golem.
4. Notice that when the Wither fires at it, it will sometimes flash red despite the Iron Golem not being able to reach that high.
A Wither at half health or below will be able to hurt itself as well, although more frequently.