Quan Chi's trickery and skills of deception were used on Scorpion, making him believe the younger Sub-Zero was the murderer of his wife and child.

Quan Chi's overconfidence, telling Scorpion of his plans after he defeated Sub-Zero, got Quantum transported to the Netherrealm.

Exactly. And to add on to this...

In the MK4 comic, it's explained that the younger Sub-Zero put on the uniform of his brother. This only helped Scorpion's confusion.

NOOOOOOOOOOOOOOOOOOOOOOOOOOOO!!!!!!!!

Quan chi is the true villain here.

If you want a production reason, I think it was tied into Mythologies and the idea of rejuvenating a Sub-Zero/Scorpion rivarly. In the story, as explained, Quan Chi simply manipulated Scorpion. This sort of began the "Scorpion is a moron" trend that a lot of fans don't like that much. His story really peaked in the first two games looking for Sub-Zero then swearing to protect his brother as atonement.