meaning - Why will I see you in Hell?

If you say, "I'll see you at the party", you mean, "You and I are going to the party and I will see and speak to you there."

If you say, "I'll see you hang!", you mean "You will be sentenced to hang for your misdeeds, and I plan to attend the execution" or even "I will take steps to ensure [i.e., 'see to it'] that you are properly punished."

But if you say "I'll see you in Hell", do you mean "You are destined for eternal punishment, which I will witness from a pleasant seat in Heaven" or "I'm so determined to stop you that I will take steps so extreme that they will cause both our deaths and even earn me damnation alongside you."

It probably won't happen any time soon, but if the occasion to snarl "I'll see you in Hell" does arise, I want to be able to do so in full confidence that I'm saying what I mean.

EDIT The collective wisdom seems to be ambiguous on whether the implication is "You are going Hell for your misdeeds, and I will help the process along by killing you" and "Your death (which I may or may not hasten) and subsequent damnation will occur before you are able to carry out your current plans."

Answer

The Shorter Dictionary of Catch Phrases (1994) defines it:

I'll see you in hell first a vehement refusal or a response to a challenge. The phrase dates from the late 19th century or earlier. Variants include I'll see you damned (or hanged) first.

This can be interpreted that it's more likely that the other person will be in hell before their claim ever becomes true. You don't necessarily need to go to hell as well.

Alternatively, it could mean you think their claim is so outlandish that it's more likely both will go to hell than it coming true.

The OED dates it to 1715, from Proceedings of the Old Bailey:

Saying G—d D—n him, twenty times over, and the High Constable too; he should see them all in Hell.

Another early quotation from 1879:

I'll see you in hell before I vote for Charlie Lake, or any other Democrat.

Finally, it can also be an expression of hatred, as demonstrated by the last quote in the OED, from a 2007 Independent on Sunday:

‘See You in Hell’ he sneered to two fellow death-row inmates he couldn't stand.