After processing and trying to understand the essence of Yuugi's grief, I realized that his nearly indescribable pain could be compared to... well, a fucking miscarriage.
Because how do you get over such an incredible phenomenon as sharing your body with something that isn't exactly a living creature, but is definitely something that exists? An incipient soul. Yuugi's body assembled the scattered soul fragments from the Millennium Puzzle pieces and created a complete soul. And then he let it live inside him. He let it grow inside him. He let it affect him and form a bond with him, until they became so deeply intertwined that it was hard to tell where Yuugi ended and where Atem began.
In some ways, pregnancy is similar. You almost literally grow together with your baby. You give them a name (Other Me), you talk to them, you care for them, and at some point, your brain becomes so radically rewired that you don't want to live without them anymore. You can't imagine a life without them. You're ready to do anything for them. Because you and the soul growing inside you have become one, and if you don't give them what they need, you begin to wither too.
Yuugi had no choice. Perhaps there could have been another way, but that would only have been self-deception. Despite his age, Yuugi was already wise enough at 17 to let go of what had to be let go, because the soul he believed was living inside him was already a dead soul.
So Atem was ripped out of Yuugi, leaving behind a hole, a wound, a void in his place that someone might try to fill with something else: hobbies, fanaticism, or the laughter of other loved ones, etc.
But you can never, ever forget the future you'd imagined with that soul, and in the end, a part of you dies with it.