Why is "don't say hurtful things" better than "gain empathy and insight into the lives of a group of people who are generally very badly off, in very large part because our country allowed them to be enslaved for hundreds of years"?

Because it seems like "don't say hurtful things" covers a lot of stuff, but you miss out on the specific empathy this specific situation gives you by reflecting on why this one word should be taken off the table for white people.