People should be reminded how melee combat works in Shadowrun.
Melee is not seen in Shadowrun as "I strike you. You dodge me. Now it is my turn to strike you back."
In reality, if you used Parry + Sword to defend against Unarmed Combat, then you would be mostly reducing their chance to successfully hit by forcing them to not attack you very often at all.
Someone with a sword, defending against unarmed combat, is mostly on the offensive. The moments the Unarmed Combat person has, will be to either try to create a weakness to exploit (feign attacks) or dodge the offensive attacks of the sword user until able to counter.
Instead, Melee is 3 seconds of martial combat. Parrying an Unarmed Attack would mostly be sitting there doing nothing, as the Unarmed combatant only gets a few attacks of opportunity on you. Otherwise, the Unarmed combatant would be sliced to pieces trying to attack, while the swordsman parries.
So "Parry" can actually be, basically, offensive attacking. Just not enough, apparently, to do even a single box of damage.