Endermen are not angered or aggravated by endermite nor do they pathfind to them
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Could you give a bit more information? How did the endermite spawn? Using commands or using ender pearl? Because endermen only get aggressive when it is spawned using an ender pearl.
I summoned an Endermite using commands, and after a minute or so, the Endeman attacked it.

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Endermen are aggressive toward the endermite when it is spawned by using an ender perl