The fuck? I must have fundamentally misunderstood how to parry then. When I try I just swing my sword in its direction. I pulled them off on regular enemies / in the tutorial etc.
Parrying is context-sensitive; you can only do it during an enemy's attack. And Raiden will only assume the pose for a second or so, so you can't just hold it and wait. It forces you to really watch the enemies and understand the timing of their attacks, but with a bit of practice you'll get the hang of it easily. Even on Hard mode, the window for just a plain parry is quite generous.
A perfect parry is when Raiden automatically counter-attacks, usually when you parry
right before an attack hits you. Those are pretty hard, so it's much safer to just go for regular parries until you can nail the timing.
Blade Wolf is definitely the game's parrying tutorial, though. You'll notice that he'll bounce pretty far away from you if you're just going for regular parries. To get him into a stunned state when you can actually dish out some damage you either have to be really aggressive and constantly chase him down, or try for perfect parries which knock him down straight away. Make sure you're locked onto him so you can always keep him on screen while he's dashing around, and remember that every attack needs its own parry (when he does his three hit combo, you have to parry each hit individually, in other words).
Oh, and generally, a red flash from an enemy's eye is an attack you can parry, a yellow flash is something you have to dodge/avoid. The yellow flashes are things like the Gekko grabbing you with that whip thing, regular soldiers trying to grapple you, etc. All Blade Wolf's attacks can be parried, though, you just have to learn the timing. He'll always give you a red flash, and usually his whole body will turn orange, so just wait for the attack and parry. The only tricky one is when he'll leap around the arena a few times before diving at you, so watch him closely (there's no set number of jumps before the attack, you just have to be ready).