For Asher's father, his difficulty accepting Asher's homosexuality has to do with legacy and his preconceived image of his son being different from reality. This plot point is still quite a way's off so I may revisit this and it may change when I get around to this part, but it is mostly a selfish point of contention that Mr. Copeland is aware is selfish and thus has trouble grappling with his feelings on it. His biggest stumbling block is not that dissimilar from Asher's own issues with wanting leave behind his mark on the world in some way, but while Asher is a creative person, and thus wants to create a work of art to be remembered by, Asher's father made his legacy his family, and it's a struggle for him to accept that it's not going to continue past Asher.