Chris Paul has always been a bit of a micromanager. When he arrived in Los Angeles in 2011, he completely changed the Clippers' culture both on and off the court. How the team functioned became a part of his identity. If Paul wanted a trade there was very likely a chance he would get it. However, when Doc Rivers arrived and took over operations for the team, there was an expectation that both sides would have to compromise.
In the case of Rivers' son however, Paul wasn't willing to budge. A reported trade that would have sent Austin Rivers to the Knicks for Carmelo Anthony was eventually shut down by Doc Rivers. Paul reportedly was already annoyed with how Rivers gave preferential treatment to his son, but the trade was what broke the relationship. Here's more from that, via ESPN's Michael Eaves:
It led to resentment within the locker room, which often played out during games. One of Paul's biggest contentions with Doc was that Paul, and other players, felt Doc treated Austin more favorably than other players. He would yell at guys for certain things during games and practices, but not get on Austin in the same manner for similar transgressions.
But what really solidified Paul's dissatisfaction with Doc was a proposed trade involving Carmelo Anthony last season. New York offered Carmelo and Sasha Vujacic to the Clippers in exchange for Jamal Crawford, Paul Pierce and Austin Rivers, a deal to which Rivers ultimately said no. That event led Paul to feel that keeping his son on the roster was more important to Doc than improving the team. So, ultimately, Paul lost both trust and faith in Doc. As one league executive put it, "Chris despises Doc."
Reports of Rivers "coddling" his son have been commonplace ever since he first traded for him. Even though Austin Rivers has become one of the better defensive guards in the NBA there is still a general sense that he's only around because his father is the coach. That's not true, but it's a reputation he has to deal with -- especially if his father is giving him special treatment.
If Rivers really did pass up on Anthony just because it involved his son then that would be incredibly unprofessional on his part. He's supposed to be running the Clippers to be a better basketball team. He can't make roster moves on personal feelings alone. If what's been reported is true then Paul is correct to be annoyed with Rivers.