He actually favours slavery, He has no problem with them though but in a conversation with him, he says elves/human who become slaves does that to help their families. He doesn't have a slave, but his house does. It's just like orlesian servants but as a slave, doing as it's master commands.
I don't think he favors it , he just doesn't understand the "no slavery" of other countries.
And he says slaves , and peasents/ elves in alienage have more or less the same situation , except slavery can offer benefit (I suppose depending on the type of slaves , some are educated for their job , and if they already have some skills can sell themselves for more)
Anyway I don't agree , even if in some cases the situation of a slave can be better than some free men stuck in ghetto , slavery is still a huge wall for human rights to bloom .So it just leads to more abuse ( seeing people as "things" is a fertile soil for atrocities afterall)
The thing is Dorian is just defending his country , in numerous banter with Sera and Solas , he sounds pretty sorry about the whole debacle.
He says he's happy to have the chance to interract with free elves (first time in his life) , also he's very sorry about the fall of Arlathan and destroying elven culture.
I think it's just a case of Dorian being short signed , because he had a life of privilege.I doubt slaves go complain to their master's son , and I doubt Dorian was hanging out with common folks.