In which case it's a parry(B), attack(B), failed parry(A).

I know what you're saying but the maneuver is impossible without the weapon, so it's subsumed within the parry action.
If I correctly read what you're saying, you're counting "evasion" as part of parrying. Which I grant it often (typically?) is, but the official definition of "Parry" is "deflecting an incoming attack." And avoiding isn't deflecting. You can certainly evade a cut or thrust without having a weapon in hand. We do this at my school as a drill, just to teach people the importance of not just standing still. We take their weapons away and make them concentrate 100% on evasions.
I grant that once you have a weapon in hand, it's very hard to separate the two, and thus they should probably be subsumed in a single "defend" action, but parrying and evading are technically different things.
Moreover, we need to discuss the difference between "single time" actions and "double time" actions. In single time, you parry and counter attack in the same tempo, to whit...
SINGLE TIME:
First tempo: A closes and Attacks. B then
simultaneously Evades and Counterattacks.
(Or alternatively, if B has two weapons (or a single one capable of doing both simultaneously), Parries and Counterattacks. Since A is already using his tempo to attack, he's screwed on a defense.)
Alternatively:
First Tempo: A Attacks. B Parries (or Evades, or Parries and Evades).
Second Tempo: B counterattacks. A Parries or Evades (or doesn't).
Repeat.
Many combat systems advocate for learning how to parry/evade and strike in single time, but it's something of an advanced move - probably best modeled as the ability to "counter-attack" on a failed attack (bringing this back to RPGs,
Savage Worlds actually has an Edge called "Counterattack" that allows a character to do this).