He had no choice. Not really.
The life he had, the one he had known was behind him of his own volition. So in that moment, the decision was made with the full understanding that it would be irreversibly gone.
Would she continue to love him? Yes, he was certain of it, but would she ever forgive him? No. Understand his actions, perhaps. But forgiveness? Never.
So in that brief moment, he gave a eulogy for himself and a eulogy for the hugs she had given, the rare moments of laughter he had shared with him, the memories of conflict and pain from early on that were soothed by her voice as she gently stroked his head. A final eulogy for him, for the one that stood there -- the last person in the way of his complete rebirth. This is how it had to be: betrayal and death in order for his self design to live.
So you see, he really had no choice.
And when his father said, "Yes, anything," Kylo knew Han truly meant it.
Kylo gave thanks and a strong farewell to himself, and his family forever, as he watched Han fall.