@HOOfan_1
Ryuu didn't put doubt in their minds, it was already there and he just made them face that head-on. Neither of them was capable of supporting the other through that and as a result, their relationship fell apart. It was ALWAYS going to end like that.
Joe has impulse control issues and delusions of grandeur, and Yuzu is...yuzu. Notice something about Joe and Ryuu? They're both as far from being her father as possible. One's a criminal and the other is incompetent at almost everything, but noth live abaout as far from the socially acceptable as possible with out being actual villains. It's pretty clear she has a type.
With Joe she has this intense emotional connection, with Ryuu she has support and long term commitment. So the question is, which disaster will she pick?