If the knight defends, the pike's counter bonus removes combat bonuses first. When the pike's +100% is applied against the knight's +20%, it removes the 20%, and then divides the remaining strength by 1.8 (the remaining 80% of bonus) yielding an effective knight strength of 5.5555. The pike has a str of 6.6 yielding a ratio of 0.8417 (from the knight's perspective).
If the knight attacks, he has a strength of 12, and the pike has a str of 12.6. From the knights perspective, this yields a ratio of 0.9524, so the knight is better off charging into a group of defending pikemen than letting said pikemen come after him (somehow
).
From this and some handwaving math (I crunched the numbers behind the scenes, but we could also prove it directly theoretically, but instead, HANDWAVE! because it's already mathy for many people) we get a general rule of, if the combat of the knight is higher than the pike, he's better off attacking.
I understand what you're saying tristan, but this is also sort of true for Conq's (or Cataphracts) and pikemen, though in that case it's more trivial. Defending vs a pikeman is bad if you have the chance to kill it on open ground.
This math also comes up with landsknechts and macemen, where a maceman with higher combat should be attacking rather than defending landsknechts. Or running away. Or finding a x-bow.