I thought Arl Tegan was pretty reasonable throughout.
He has reason to distrust an organization with an army, not just on the border of his nation, maintaining a hold on sovereign Ferelden territory two years after they should have relinquished control.
Later, he has more than enough reason to be angry when the Inquisition all but declares martial law over the Winter Palace, and doesn't disclose the nature or scope of the Qunari threat until it is almost out of control.
Really, while the Inquisitor shows themselves to be personally competent as a combatant, the organization shows itself to be everything the nobles have reason to fear it is. The Inquisition has a hammer, and not only does everything look like a nail, they start to believe that they are the only capable carpenter. And that's before we find out that every elf in the organization not named Sera or 'Dalish' is either a Qunari spy or a Solas spy.