Remonstrate means to call someone on something that's wrong. If your mother yells at you in public, you might call this getting chewed out. She might call it remonstrating. Either way, it's embarrassing.
Remonstrate has its roots in a Latin verb meaning "to show," and it used to mean "to make plain." Which is why remonstrate is a word that puts the glow of respectability on the action of yelling at someone or telling them that they're wrong. The sense is that the person remonstrating is the victim — they're just making the injustice plain.