There's no reason WHY other than that's what the creators wanted them to do, same as why sunlight kills skeletons, or why Creepers explode.
Their early behaviour was based on the 'Weeping Angels' from Doctor Who, creatures that couldn't move while they were being looked at. So their current behaviour is just something based on that.
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You cannot tame an Enderman in Minecraft. If you don't look at them, they will not attack you though. If you wear a Pumpkin on your head, they will not attack you, regardless if you look at them. But be warned, if you hit them, they will attack you.
Enderman kill you ONLY if you attack them. There might be another way too.
The fanmade enderman is a version of the enderman MOB in Minecraft 1.8. The fanmade version of the enderman was popular because it was released before Minecraft 1.8 came out. Since the release of Minecraft 1.8, the fanmade enderman is obsolete.
No. a Enderman is based on a slenderman. Notch wanted to make the Enderman look a bit more frightening than a mutated Steve
In Minecraft, Endermen are mostly neutral, on both creative and survival mode. But if you try to attack them, they will fight back.