Funny that you should bring this up, since I just read these two scriptures again recently, and at first glance thought they contradicted each other. But they don’t.
"Doesn't one of these ancient proverbs encourage engaging in debates with those unwilling to be persuaded and at the same time the other say doing so will only drag you down with them?"
In the first Proverb, the fool must be expecting some sort of answer; so, its basically saying, don’t answer a fool like a fool. (Matt 5:41) The second one seems to be saying, bring out the fool’s folly when you answer. So, in both cases, someone who is spiritually wise, would answer a fool with wisdom. If one is using spiritual wisdom and they choose to “debate”, I don’t see how in either case, the person would be dragged down. Sheesh, myself and many continually bring out the foolishness of the GB, and I know they read it, when I personally write it elsewhere. They just don’t want to have a face to face “debate”! They are wise enough to protect their own foolishness. (Prov 17:28)
These are interesting renditions of Prov 26:5 –
“Answer [and correct the erroneous concepts of] a fool according to his folly, Otherwise he will be wise in his own eyes [if he thinks you agree with him].” AMP
“Answer fools when they speak foolishly, or they will ·think they are really wise [L be wise in their own eyes; C a wise person must read the situation to know whether to answer or not].” EXB
The apostle Paul: “We demolish arguments and every pretension that sets itself up against the knowledge of God, and we take captive every thought to make it obedient to Christ.” 2 Cor 10:5