I think its just the opposite of what some of you are thinking. The wardens aren't "killing" the Old Gods in his mind, they are freeing them. In the tales, Fen'Harel locked both the 'good' gods and the 'bad' gods away. We now know that that the old elven Gods are not exactly benign all-powerful entities, but were likely very powerful elves themselves. They also had factions that warred with one another. The game also tells us that powerful spirits ALWAYS return.
Fen'Harel probably locked one the life sparks of one of the factions away in Dragons and buried them deep underground. The other he locked beyond the veil. Now you have the Wardens going around KILLING the Old Gods 'traps' and freeing those life sparks. Solas seems to be an all around good guy and likely locked the two sides away from each other to prevent some major catastrophe from happening. The Wardens are in effect speeding along the undoing of his work.
So that's why I believe he doesn't care for them much. He basically says what the Wardens are doing will lead to a greater doom down the road. He has no love for the blight, which I believe is the 'dark' gods attempt to free themselves.
Those are my thoughts on it anyway.
I'm pretty sure Solas wants to undo the banishment of the gods if anything. Restore what was lost, and all that. I mean, he even suggests that he was not quite happy with how things turned out when asking a hypothetical question to the Inquisitor.
"You would risk everything you have in the hope that the future is better? What if it isn't? What if you wake up to find that the future you shaped is worse than what was?"
At least that was my interpretation of it. So going back to the Gray Wardens, I think Solas objecting is possibly as simple as he makes it sound. What they're intending to do, and not so much the method, could have worse consequences than the Blight they intend to stop by going on their old god killing spree in the first place.
Also, correct me if I'm wrong but I thought the old gods that get corrupted into arch demons were different from the ones Fen'Harel banished. But assuming they're not, I suppose that would explain his objections even if he intends to free them. Them being dead would make it more difficult, I mean.