The Archangel assault was a pretty big deal even if the events of Dead Beat blew it out of the water and as far as the WC was concerned it could be laid at Dresden's feet for starting a war, and then he showed that in the decade+ since he heard about the WC he never tried to get fluent in Latin despite presumably having more comprehensive options than a correspondence course.
The robes were just another nail in the coffin after that.
Except Harry didn't have anything to do with the attack on Archangel. That was on Eb, his decision to attack after Simon was killed. Eb may have used Harry as part of his justification, but Harry had nothing to do with it.
Um, Latin isn't exactly something you can take a "conversational" course in unlike Spanish or some other languages. There is a difference, some classes concentrate on the written and people can take more than one year of say French but never be able to speak it well. Since Latin isn't spoken anymore, it would be difficult without help to be fluent. Also do not dismiss how depressed Harry was, he could have used both medication and therapy.. Being that depressed, he isn't going to give a damn what the Council thought of his bathrobe.