It's not about coffee
The feud which leads to this match stems from an incident where Chris Jericho, excited over the newest CD from some band called Fozzy (I doubt they'll go very far), bumped into Kane and spilt his coffee all over the Big Red Machine.
I can guarantee that, were this to happen on the campaign trail, Glenn Jacobs would most likely be more than gracious; rather than a beating, the worst one could probably worry about in that confrontation would be a lecture on the virtues of limited government. This, however, was not the campaign trail, and rather than his best everyman blazer, Kane was wearing a mesh tank top from the back of every Gadzook's store in every mall in America.
Telling Jericho he had no idea what it felt like to be burned, Kane made a total fiscal overhaul of the nearest catering table, sending drinks and cups flying in what's probably a metaphor for government waste.
Kane would later elaborate that, no, spilled coffee was not the reason he would like to mangle Jericho at Armageddon; rather, it was Kane's hatred for Jericho's good looks, charisma, blond locks, popularity, band (to be fair, "Judas" was another 17 years away, so maybe Kane had a point), and fundamental misunderstanding of the ins and outs of the Austrian economic system.