Deductive arguments are useful, but limited in application. When it comes to the truth of a matter that relies on observation, evidence, and conceptual clarity, then negative arguments become logical traps. Worse still is if the entire case is based on a negative argument, then all the argument becomes is an argument for ignorance. It might all logically follow, but it would tell us nothing useful about the position that's being argued for. I'll illustrate this with two examples.
First, suppose there's an argument that tries to deductively prove that the universe had a supernatural origin. A deductive argument could go something along the lines of "If the universe didn't come about naturally, then it must have had a supernatural origin", fleshed out with reasons why a natural origin is a contradiction. The problem with such an argument is two-fold; firstly that one cannot rule out every possible natural scenario so it could never be satisfied, and secondly that supernatural isn't adequately defined except as "not natural". The argument doesn't tell us anything about how the universe came about.
Second, consider the Euthyphro dilemma. It's as effective a deductive argument as there could be, smashing apart the notion that the divine has any part to play in morality. But what could we say from there? That there's no such thing as morality? That it justifies the position of the person who brings up the Euthyphro dilemma? Of course not. Whatever case there is for morality isn't settled with that argument, it just rules out what a case is not.
The greatest danger with negative arguments is that if one's position is dependent on the contrary being false, then there is the danger of falling into an argument from personal incredulity. And to me, that's why it's important to focus on making a positive compelling case, and seeing negative arguments as a way to tease out implications of particular lines of thought. Otherwise we are dressing up ignorance as explanation.