>>527354330
I always headcanoned it as Chara being a self-hating little shit and not wanting to be considered part of the family because they feel like they dont deserve it (despite deep down desperatley wanting it)
And Asgore being thick-headed and unable to see beyond Chara's words at face value just goes, okay I will respect you decision and not consider you my child ]=)

of course there's no real evidence for it, it's just how I interpret it