WAI as per https://www.minecraft.net/en-us/article/minecraft-snapshot-23w51a

You currently can't dispense wolf armor on wolves, which makes it inconsistent with all other armor (player armor and horse armor).

Steps to reproduce:

1. Place down a tamed wolf.
2. Place a dispenser and button next to the wolf.
3. Put a wolf armor item inside the dispenser.
4. Press the button.
5. Notice how the wolf does not get equipped with the wolf armor, and it drops the item instead.

See the attached video as well.