If you think something or someone is worthless, and show it, you behave contemptuously: you're being disrespectful and mean.
The word is all about showing your dislike and disrespect. We may dislike a great many things, but we are not treating them contemptuously until everyone else around us knows exactly how we feel. Acting contemptuously is putting on a little show, almost like a toddler's temper tantrum, though with more thought behind it. A student who treats his teacher contemptuously is going to be in trouble, and an employee who treats his boss contemptuously might get fired. Contemptuously is the opposite of respectfully.
