AC the Cross-Product is not the reason. It's just the maths used in those circustances. The reason is in my post. Just using the cross product without understanding why is as bad (or just as good) as using the term Gyroscopic Precession for the behaviour of a rotor disk - it just becomes a rote learnt process for predicting a result without the understanding part having to trouble the 'victim'.
(perhaps you missed the italics on my post for the word because - the quote is without them)