Why did Walt tell Skyler he killed Hank in Breaking Bad? Was Walt trying to send a message? Was he trying to protect Jack's men?
The conversation between Skyler and Walter in Ozymandias about Hank goes like this:
Walt is raving at Skyler, knowing full-well the police are listening:
Walter: ..Toe the line, or you will wind up just like Hank.
Skyler Walt. Tell me what happened. Where is Hank? Please. We need to know.
Walter: You're never gonna see Hank again. He crossed me. You think about that. Family or no.
Skyler (SOBS) Oh, God.
Walter: You let that sink in.
Skyler Walt. (SKYLER SOBS) I just want Holly back. Please, Walt.
He never actually states that he killed Hank, or even specifically that Hank is dead, but he implies it so that:
- It makes the threat to Skyler scarier, reinforcing that whatever she did was done under duress.
- It supports that Skyler had nothing to do with what happened to Hank and helps further distance her from Walter's legal problems.
The white supremacists are far from his mind at that point, it is all about what's best for Skyler and the family.
If this is about the phone call after he took Holly, the reason for the call was that he knew the police would be listening and he wanted to make them believe that Skyler was not a willing participant in any of his criminal activities.
It was all fake, and she understood that. Some of the things he said were inconsistent with the facts Skyler already knew. All of it was inconsistent with his personality (both of them!) Skyler was out of character too - quietly listening to him rant on and on, instead of arguing. It wasn't planned, but she figured it out fast enough to play along.
This conversation took place on phone when Waly calls Skylar after Hank's death. I don't think Walt ever said that he killed Hank. If I correctly remember the exact dialogue he just said
"You are never going to see Hank again",
after which everyone bursts into tears, including Walt. Everyone knows that Hank was about to arrest Walt but Walt was still free and he said that Hank would not be seen again. So everyone concluded that Walt killed Hank, but no body knew what exactly happened. He was definitely not trying to protect Jack's men. Why would he? At that moment he was himself a man running from law, a man who had lost his family, who had lost his money and who was responsible for getting his family member killed. Walt was in shambles at that moment and his telling of Hank's death was filled with grief and remorse. At least this is what I can infer from the scene.
My take was that at that point, Walt felt the only way he was going to keep his family together and potentially win back Skyler was to be 100% honest with her. He pretty much told her everything in the last season, except for a few minor details. Plus, Jesse was still alive and Jack had his cash, and he knew he had to come clean before she found out from someone else.