Why will I see you in Hell?
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.
The version I know is "I'll see you in hell first!", which Partridge (citing Skehan) defines as 'vehement refusal' and dates to 'latish C19'; but the discussion here finds it in 1838. I have always taken it that 'see you in' here was used in the sense of 'take steps to insure that you end in' - so the phrase would mean "I'll kill you before [I allow you to do such and such].
However, the initiator of the discussion at the second link above insists on a 'modern' understanding of the phrase, without 'first', as
something more like: "I may be going to hell I may be guilty of bad things but so are you, and you, not only are you about to die, you're also going to hell, so bwahahaha!".