Why do modern-day liberals (for example) generally consider it okay to say "I think everyone should be happy" without offering an explanation, but not okay to say "I think I should be free to keep slaves", regardless of the explanation offered?

"I think everyone should be happy" is an expression of a terminal value. Slavery is not a typically positive terminal value, so if you terminally value slavery you would have to say something like "I like the idea of slavery itself"; if you just say "I like slavery" people will think you have some justification in terms of other terminal values (e.g. slavery -> economics -> happiness).

So, to say you like slavery implies you have some justification for it as an instrumental value. Such justifications are generally considered to be incorrect for typical terminal values and so, the "liberals" could legitimately consider you to be factually incorrect.