“Thus says the Lord GOD: Because Edom acted revengefully against the house of Judah and has grievously offended in taking vengeance on them,  therefore thus says the Lord GOD, I will stretch out my hand against Edom and cut off from it man and beast. And I will make it desolate; from Teman even to Dedan they shall fall by the sword.  And I will lay my vengeance upon Edom by the hand of my people Israel, and they shall do in Edom according to my anger and according to my wrath, and they shall know my vengeance, declares the Lord GOD.
(Ezekiel 25:12-14 ESV)
So far, each land/people group that God is correcting has been so for a different reason. Edom is being disciplined because she "acted revengefully against the house of Judah and has grievously offended in taking vengeance on them."
You know that saying... Vengeance is Mine Says the Lord.
I think it holds true eh? We shouldn't be in the business of handling vengeance. We don't know the whole story behind things anyways. Each situation in life has it's own subplots. There is no way we can truly know them all.
BUT the fact is this. Edom acted out in vengeance against the Lord's people, therefore the Lord will stretch out his hand against them and make is a desolate place. Its people and animals cut off. He will do this by using the people of Israel.
I find it interesting in these verses that God doesn't add "so they will know that I am the Lord". I wonder why they are not here. He has the people of Israel act out his anger and wrath upon Edom because they sought vengeance on his people. This is as far as these verses take God's discipline.