To wade is to walk through water. If you've been fishing without a boat, chances are you've gone for a wade to reach your precious prize (and if it got away, exaggerated how big it was.)
Wading doesn't have to be literally through a liquid; any action that involves a laborious slog through something that offers resistance is a wade. Just try reading Moby Dick. And if you want to get into a fight? Wade right on into the brawling crowd. Or if its verbal fisticuffs you're after, wade right on into the debate.
