Fisking is a written argument where one person sequentially addresses each point of an of another person's argument.
This is done in a precise manner relying on semantics and ambiguities to infer a defect in the original point. This approach is tantamount to taking a sentence out of context in order to refute an entire argument.
Fisking does not pay heed to the opponent's thesis as a whole, and thus does not disprove the thesis as a whole.
That bastard was Fisking my posts. So I had to create a hydra to Fisk him. I really fisted that Fisking fucker.