Briefly, because this is a Sons of Anarchy question that’s coming up in referrals, and there’s reason to be confused. (SPOILERS)
Jax doesn’t want to kill Juice because he thinks that Juice killed Tara, or because Juice killed Eli Roosevelt. If that were the case, the threat against Juice would’ve disappeared after Jax tortured and murdered the nice young Asian man who clearly loves his mother, who Gemma wrongly pinned the murder of Tara upon.
The reason that Jax wants to kill Juice is because Juice betrayed him (again). Last year, in the penultimate episode of the season, Bobby recommended that Juice take some Oxycontin to deal with his pain. Juice did so, but he took way too much oxy, and nearly died of an overdose.
However, under the influence of the oxy, a groggy Juice confessed to Nero that he’d killed Darvany (Samaire Armstrong), the wife of Nero’s cousin, Arcadia (Dave Navarro).
See, way back in the early episodes of last season, Nero had killed Arcadia because he had no choice, but Nero had wanted to figure out how to spare Darvany, who was the mother of the kid that shot up the school. Jax basically said, ‘No way!’ because he was worried that Darvany would connect the club to the gun that the kid used to shoot up the school. Darvany was a drug addict, and clearly dangerous. So, behind Nero’s back, he ordered Juice to smother Darvany to death with a pillow.
Once an wacked-out Juice relayed that information to Nero, he betrayed Jax (he also, obviously, created a lot of tension between Nero and Jax, which will no doubt play out in the coming episodes).
And that’s why Jax wants to kill Juice.