Simple rule, people. “That” refers to things, “who” (and “whom” – but that’s another discussion) refers to people.
A pet peeve of mine, one that I have been noticing a lot lately, is the use of “that” when referring to people, instead of “who.”
She’s a person that looks good wearing green.
It’s your brother that said let’s go to dinner.
Who, people, who. Not that. Your brother and the unnamed woman deserve who. They are not inanimate objects to be tossed around.