Because the problem is no matter what he says, his family doesn't appear to be receptive to anything he's saying

It's not like Junior was going to change his tune if Walt had only said, "Wait, son, I didn't kill your Uncle Hank, it wasn't me and I'm gonna prove it"

Junior and Skyler aren't suddenly going to flip and join Walt's side

So I'm not sure what him correcting that piece of information gets us at this time, or even down the line

I could be wrong, but it seems as if this family is beyond repair at this point, which is what Walt realizes and leads to him finally breaking down calling the police on himself

And anyway, it appears Walt's more concerned that his name's being erased from the history books by the Grey Matter folks

At this point in the story, soothing his ego and "getting justice" is more important than clearing his "innocence" (*coughbullshitcough*) with his family when it comes to Hank's murder

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But Zootown, black people and media, so...