Ir Abelas, Vhenan.

Thats easy enough to figure out isnt it? Considering when the two of the 3 only people he truly considered his friend were killed by someone elses hand (Fellassan was killed by Solas which is why i didnt include him in this example) he went nuclear on those who did it. One was purposeful in the pursuit of power and ambition - Mythal who was killed by the evanuris, and Solas himself mentions in Tresspasser "A crime for which an eternity of torment is the only fitting punishment."

The other was when his eldest friend WISDOM was corrupted by the mages.

The mages didnt do it purposefully, or cruelly, they wanted to summon a spirit to protect themselves, and in doing so ignorantly forced a spirit in chains and corrupted it till the only option Solas had was to give them a merciful death. What was Solas judgement anyways?

Death. He killed them all with no regrets to having done it, only regret in having to end his friends.

Solas hates more than anything is people ignorantly squandering what he worked hard and had to sacrifice, which makes sense since whats the antithesis of Wisdom? Ignorance. (and Solas was a spirit of wisdom, so..) Solas described himself as hot blooded and cocky and always ready to fight when he was younger, but that anger never really went away entirely. In Tresspasser he mentions about the Qunari agents "...There is no benefit in allowing harm come to innocents before its necessary. And the Qunari offended me."

And when Rook disrupted the ritual? He was 100% ready and wanting to kill them ( Theirs cut dialogue of Solas saying he would kill Rook, coudnt find the gif of it but the dialogue is easy enough to look up), he didnt hesitate using blood magic and the entire time was slowly preparing to swap with Rook and cast them into the regret prison indeffinetly. Solas isnt a black and white character, he is complex, nuanced, and with contradictions out the wazoo as real life people are. He doesnt do anything seemingly for any one reason - he does it for multiple. And one of them - when killing or harming someone he loves - is always a form of retribution over a slight against him. When Solas killed Fellassan and Varric it was by his own hand - his own choice and a necessary sacrifice in his mind that was easier to bear. But if someone else wouldve done it? I bet you Solas wouldve hunted them down and made them pay for it personally. A low approval INQ gets Solas to admit he never had friends before besides spirits - which Mythal was before taking form, and Fellassan was arguably his only friend before he sacrificed him.

The main reason I think Solas refused to allow Lavellan with him? In each of these scenarios someone he loved was weighed against his powerful sense of duty and regret and lost. He killed Mythal to regain power to free the elvhen people still in uthenara slumbering beyond the eluvians and rebuild the elvhen empire by tearing down the veil. He killed Fellassan when Fellassan saw the modern elves as his people worthy of being saved - he threatened Solas mission as he knew Fellassan's fondness for Briala, and refused to give him the eluvians, so he killed them. He killed Varric at the ritual site, and I dont doubt it was a heat of the moment thing when he turned the blade, but i think Solas was honest, atleast in not meaning to kill Varric - as he paused a long time while the ritual was falling apart , just staring where Varric had fallen before the evanuris emerged. If he had let Lavellan come with him? There is a strong chance at some point either Lavellan would be able to convince him to stop the ritual (thus compromising his operation) or something could have gone wrong and he would have to chose (AGAIN) to scarifice his duty to his people or someone he loved, and Solas mentions himself to Lavellan in INQ "Loosing you would.." implying how devasted he would be.

Then the letter he wrote for her in VG mentioning he never forgot or stopped thinking or loving her this entire time, and would always love her "What I feel for you will never change." (adding this little blip from @s0lavellan )