In Rostand's Cyrano de Bergerac, Cyrano is not a character who hides what he believes or how he feels except in one area of his life--Roxane, of course. Aside from his love for her, Cyrano is fairly straightforward about what he sees as right and wrong, good and bad. The incident with Montfleury is a great example of that. Cyrano gives two reasons for his disgust.
Montfleury is a bad actor and an insult to good theatre. He is unpleasantly corpulent and overacts when he is on stage. This is the first reason which he cites for all to hear. The second reason he does not share until he is alone with his friend Le Bret after Montfleury has run off and the theatre has been cleared. Cyrano says he is displeased with Montfleury because
while he stammers through his little piece,
[he] makes sheep’s eyes with his frog’s eyes, if you please!
I hate him since he allowed himself one night
to raise his eyes to her ...
Though Le Bret does not know and Cyrano does not say, the woman Montfleury dared to be flirtatious with is Roxane. This offensive act is part of what gets Montfleury booted from the stage.
Cyrano is willing to spend his last coin, which he literally does, to defend two things he loves and values: the arts (theatre) and Roxane.