Using 'cavalier' to describe someone's behavior suggests that it's negative and irresponsible. His cavalier disregard for safety worried everyone.
Pro Tip 2/3
Often Critical
When 'cavalier' is used, it often implies that the speaker is critical of the carelessness shown. She was cavalier about spending money, which led to debt.
Pro Tip 3/3
Not Always Intentional
'Cavalier' can describe unintentional carelessness, not just deliberate disregard. His cavalier mistake during the experiment ruined the results.