Infantile means childish in a negative way, like a baby or very young child. When someone acts infantile, they're behaving in an immature way that doesn't match their age. A teenager throwing a tantrum because they can't have dessert before dinner is acting infantile. An adult pouting and refusing to speak when they don't get their way shows infantile behavior.

Infantile specifically describes babyish behavior that seems out of place. There's a difference between being playful or having fun (which people of any age can enjoy) and being infantile. Playing tag at recess is playful. Crying and stomping your feet when you lose at tag is infantile.

In medicine, doctors sometimes use infantile to describe conditions that appear in infancy, like infantile spasms, a type of seizure that affects babies. But in everyday conversation, calling something infantile is usually critical. If your teacher describes an argument between classmates as infantile, she means both students are acting like toddlers instead of using their words and problem-solving skills. The word suggests that someone should know better and act more mature given their age and abilities.