The father should not have disowned the son, but it would be a hard position to be in if you have a strong moral objection to homosexuality. I am not sure if there is a situation that merits disowning children, even if the children become serial killers. You can cut off a child physically, but those emotional, and possibly spiritual, ties remain.
The father is only doing a disservice to himself, as the son did a disservice to himself by publishing the letter. By publishing the son is merely affirming the position of the father- that the parent/child bond is not sacred. However, the son obviously was very hurt and wanted to get back at his father by publishing the letter, something he will live to regret as well, no doubt. I am guessing they had a pretty superficial or poor relationship to start with.