Logical contradictions in an argument can only be sufficient in refuting said argument, if the argument itself is constructed entirely by classical logic aka "formal logic". This is because formal logic necessarily accepts the Principle of Explosion.
In contrast, arguments constructed with paraconsistent logic cannot be refuted by pointing out contradiction. This is because paraconsistent logic does not accept the Principle of Explosion.
Why is this important? Because classical logic cannot always be used to understand something. In other words, some things cannot be understood without accepting contradiction and thus require the use of paraconsistent logic. This is best illustrated in the case of paradoxes (the Liar Paradox, Zeno's Paradox of the Arrow, Russell's Paradox, Sorites Paradox, etc). What's apparent here is that many of these Paradoxes are pertinent to reality and not just rhetorical.
Given that this is the case, it is important to make a conscious choice (rather than simply apply classical logic as a default in all circumstances) as to which type of logic to employ when trying to understanding some phenomenon or when trying to make an argument for (or against) something.
Making this conscious choice would fundamentally alter the nature of our arguments.