He's letting Ken rest on him because it's what Ken needs; it's something he's doing for him. That way of thinking means Minato could do this forever. It's almost like he, himself, isn't personally involved.

"Just because it started out as a lie doesn't mean it needs to stay that way." It's spoken in a murmur as Minato turns it over in his head. "Killing something preying on others is a natural urge. If you were doing it for your own reasons... that you understand that now means you can decide your reasons for yourself."

Ken growing to understand himself means that he can be self-determined. It's a process Minato's watched every social link he's had go through: in the beginning, allowing others to dictate who they were. Or allowing their own helpless feelings to do that. Ken being caught in grief and rage fulminating into a need for vengeance wasn't so surprising. But Ken has grown a lot, has seen inside himself to the uglier parts and clearly been greatly affected by that.

He has an opportunity, to make up his own mind, clear-headed, about who he wants to be.