Imagine, you're in a debate. The other person is obviously intelligent, but would rather bog things down in semantics than understand a point and move on. They begin to ask broad questions about the meanings of words like "necessity" which of course what is necessary can change depending on situations. They know what's meant, hell, you've even defined it, but they come back to it again being intentionally obtuse in order to make you sound like you're advocating something vile.
(1) willfully determined or disposed to go counter to what is expected or desired; contrary
(2) Showing a deliberate and obstinate desire to behave in a way that is unreasonable or unacceptable.
‘Kate's perverse decision not to cooperate held good’
In the OP's example:
William's perverse refusal to accept common definitions of essential words or even to work towards definitions we could all accept, sabotaged the debate, which ended in acrimony.
They are using a red herring, as best I can tell the specific ones would be the “straw man fallacy” and/or “Equivocation”