Shakespeare does not give any reason why the original Thane of Cawdor commits treason and fights alongside the Norwegians. All the reader knows is that he did turn traitor, fought for the Norwegians, lost, was captured, and executed by order of Duncan.
If I had to defend his actions, I would say that he turned traitor because he thought he would be fighting for the winning side. It is exactly what Benedict Arnold did during the Revolutionary War. He started out fighting for the colonists, thought that he was on the losing side, and defected to the British army. I'm sure the Thane of Cawdor thought the same. He would win. He had to have thought that, because he knew that his loss and capture guaranteed his death.
It's also possible that he turned traitor because he knew some dark secret about Duncan and no longer thought that Duncan was as honorable a king as everybody else thought.
It's even possible that the Norwegians promised the Thane of Cawdor land, riches, etc. He knew that he wasn't likely to gain more power under Duncan, but there may have been more "upward mobility" if he aligned himself with the Norwegians.