Lies. His relationship with his son was based on lies. Gabriel Agreste hid something from his son and his son hid things from him.
They say that you should raise your children with an iron fist, that they'd grow up into good, kind and honorable men, but if so why did it seem that the more he squeezed, the more Adrien wanted to flee?
Why was it that all the important people in his life seemed to vanish and disappear? With that thought in mind he squeezed even harder.
He was suffocating his son, and he knew it too, but he just couldn't bring himself to stop because he didn't want him to disappear, just like his mother, the love of his life that disappeared and left him with shattered piece of his heart.
When he started as Hawkmoth it was simple, take their miraculous, they will grant you a wish and you'll have your perfect family back, but things have changed, for some reason or another the akumas are becoming more violent, his head is constantly pounding, he has a few blackouts and just can't explain why, and there is a nagging suspicion that chat noir is somebody he knows.
There is also work, so many things to do, to much things to oversee that he doesn't have time left for his son, so he hired Nathalie to stay and care for his son in his place, so much for that idea she barely talks to Adrien, and when she does talk it's with her cold, robotic voice that send shivers down his spine.
His mind would whisper "Wrong, her voice is wrong she never spoke like that before, what happened to her warm, bubbly voice? The one that could sooth my soul and that could ease my worries away" and then he'd remember that it wasn't the same person talking, that wasn't his precious wife, that she was gone, and that this was just another stranger working under him and each day he realised that she was gone his heart broke just a little more.
And slowly his head was becoming a mess, a clutter of thoughts that made no sense with a single objective: find the miraculous.
But it was fine, he was fine, a little more now and it'll all be over, a little more, just a little bit more.