As Sower of Discord enters the battlefield, choose two players.
Whenever damage is dealt to one of the chosen players, the other chosen player also loses that much life.
You must choose two different players. You can be one of those players.
Sower of Discord’s triggered ability causes the second player to lose life. This isn’t damage and it’s not caused by the source that dealt damage to the first player.
If Sower of Discord is dealt lethal damage at the same time that one of the chosen players is dealt damage, its ability will cause the second player to lose life.
If Sower of Discord’s controller is dealt damage that causes them to lose the game at the same time that either of the chosen players is dealt damage, Sower of Discord’s triggered ability won’t resolve and the other chosen player won’t lose life.