When you throw snowballs to a mob it seems like it damages him, but is impossible to kill with snowballs. But there's a mob that you can kill it with snowballs: The Ender Dragon.

If the Ender Dragon is the stronger mob in Minecraft it wouldn't take damage from snowballs.

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Steps to reproduce the bug:

1. Spawn a ender dragon /summon EnderDragon.
2. Throw him snowballs or eggs.
3. Look at his life bar and you will see that he takes damage.