And here are the definitions I liked from MW, wwh. I remember well that discussion here on AWAD:

3 a : characterized by often imperious or arrogant self-assurance <how insolent of late he is become, how proud, how peremptory -- Shakespeare> b : indicative of a peremptory attitude or nature : HAUGHTY <a peremptory tone> <peremptory disregard of an objection>