Forgive me for using your well-meaning post as an example of the problems we have with language in today's media-saturated culture, but regardless of your good intentions, several of the things you said as fact simply can't be proven true.
First, you claim as fact that his profession "requires him to use coarse language and racial slurs from time to time." This statement is clearly not fact, it is one opinion among many. The case can certainly be made that he can effectively catch criminals without using bad language — it's probable that only an authoritative tone of voice when he commands them to surrender will work just as well.
Next your post says, "He was merely pointing out to his son that he did not want somebody in the family making a big deal out of it every time he did so. This is a perfectly reasonable position and really has nothing to do with racial denigration or the individual girl involved." Again, absolutist words — "merely", "perfectly", "really", "nothing" — are used to describe a situation with many shades of gray.
I'm not trying to pick on you; I believe most of us here understand that your remarks were made in the vernacular, everyday language most of us use. I'm trying to make a point about language usage. Dog was doing the same thing — using his everyday frame of reference. However, most people today do recognize the sensitivity of the n-word, as Dog himself did. That's where this situation breaks down.
The word is a bad word. Dog's other frequent frame of reference, "m****rf****r, is a terrible image that should offend virtually everyone, and he uses that one during almost every bust against a male perpetrator, without losing his show. But the n-word is directed at an oppressed people who have been freed only in stages, thus it has an extensive political lobby backing it up.
The n-word is a particularly offensive word, and it's hard to make the case that the person who uses it, black or white, isn't accountable for offensive speech aimed at a person's race rather than their character. When he called her a "whore", nobody got upset. This word was understood to mean that he doubted her character as being a person who would sell a thing of great value cheap. As it turns out, she did encourage Tucker to do just that, in selling out his own father at any price.
But Dog's specific use of the n-word in this situation implied, without stating it, that most black people are persons of bad character; or that her bad character was somehow associated with the fact that she is black. That's where he went off the rails. Even if he had said, "Son, in my experience some black people in high-pressure situations with white people can be suspicious that everything we do is about race, and she seems a little insecure this way, and this will cause us trouble," it would have still caused a firestorm, but would have been harder for Tucker and the girlfriend to use against him. He was impatiently using the n-word to try to telegraph all of that in shorthand, instead of sitting down with his son and having a counseling talk face-to-face, and it didn't work out for him.
Well, he is less in the catching criminals business and more in the entertainment business, these days. He has made quite a lot of money by projecting a certain public persona. That persona is coarse and uses foul language and slurs as a matter of course. He is in a very unusual position in that using the N-word really is part of what makes him successful in his field.
Such is the state of our culture.
Having a one-sided conversation like this into an answering machine is just stupid. I will grant you that.