The simple reason is that Palpatine has very different priorities than the leaders of the republic. The Arc-170 was designed to be a powerful, efficient fighter, while the TIE was clearly designed in response to the new evidence that Jedi are weak to hexagons.

Clear proof can be seen in the name of the order to kill the Jedi, and on page 758, line 9 of Star Wars: The Prequel Trilogy, by Terry Brooks, R. A. Salvatore, and Matthew Stoker.

New Imperial Doctrine favored overwhelming the enemy with raw numbers. With the Clone Wars over, most battles fought by the Empire would likely be against insurgents, with inexperienced pilots flying old and slow ships. TIE Fighters could be produced for the fraction of the cost of an ARC 170, and outmaneuver slower ships.

Some of it was also spectacle. The arrival of a swarm of 100 TIE fighters is far more impressive than the arrival of a dozen or two ARC 170s, even if they had comparable strength. The transition from Clone Troopers to enlisted pilots also spurred a desire for single pilot ships.

I would disagree with everyone and argue that it's about projection of power and more importantly, the method of combat.

There has been much speculation as a result of the Yuzzhan Ving invasion as to how the Empire would have responded. Many theorists have argued that the Emperor would have thrown more ships into the fray to stop the enemy at any point. Others look at the lack of shields and the elite ability of TIE Interceptor pilots as to why he would have done well. Finally others look at the empire's lack of shields (which caused many problems for the Republic in the early years) as to being more able to fight.

The change goes to sadly a more disposable military. It shows that the enemy doesn't matter because the soldiers that are being used don't matter.