Solas does not like the Chantry. This is why he wouldn't like someone who allied with the Templars, rather than just using and then disbanding them. He can respect certain individuals, like Cassandra, because he knows she is sincere and trying to do good, but he still doesn't like the organisation. When replying about the use of the Well, I tried the option let's not get ahead of ourselves, we need to defeat Cory first. I got disapproval for that and then he said something about me having to decide whether to destroy the Chantry or not. That seemed odd because there was no particular reason why having the Well would make that any easier and whilst I was in a position to vote for my preferred Divine, which might ultimately result in the Chantry imploding, I had not been given the option of actually doing away with it. So considering at that point he was already planning on leaving, I assume that bringing down the Chantry was something on his mind.
Solas also hates Tevinter, not because of what they did to Arlathan (because he knows they didn't) but because of the slavery of all races, including spirits, using the power they scavenged from the wreck of Arlathan to do so. When Dorian say he is sorry what Tevinter did to Arlathan (before he knows any different), Solas replies that if he is really sorry he will free the slaves of all races in his country. Since it has been indicated the next game will take place in the north, I suspect that he has plans that involve bringing down Tevinter. If, as was suggested in the codex in the Temple of Mythal, Solas is really a god of rebellion, then in a way his People are whoever is being oppressed. So "my People need me" could mean the ancient elves still alive, like Abelas, or it could simply mean anyone who is enslaved and needs freeing. Of course he also hates the Qun for similar reasons.
I wonder if Cory was able to trick him because of this desire to free slaves. Whilst Cory is an ancient Magister, Calpurnia was a former slave who hated the mistreatment of slaves. Cory was apparently able to trick her into serving him, until she discovers that he was planning on making her a slave again, when she turns on him. So may be something similar happened with Solas.
I also think that the linking of that stained glass window in Redcliffe positively with Shartan and its resemblance to Solas tarot card means that even if Solas wasn't actually Shartan he may have been an inspiration to him and Andraste. (My money is still on Fen'Harel posing as the Maker). Flemeth spoke of a reckoning to come that would shake the world and seemed content to surrender Mythal to Solas to bring this about. I suspect that the world shattering events will include revealing the truth about Andraste and a renewed assault on Tevinter, which will bring about the fall of both Chantrys, Black and White, or at least that is the plan. I think it will also involve the release of the last two old gods, the god of secrets and the god of death, which will not be good news I suspect. I also have a feeling that Flemeth/Mythal had an agenda of her own which means that ultimately she will betray Fen'Harel in order to get the revenge she desires.
If Solas didn't like or respect you, take comfort from the fact that you may ultimately have to kill him (whether you want to or not) and his plans seem to inevitably not end how he intended them to.