they changed the core gameplay from focusing on arcade style vs. play and free play to a more mission oriented "Dance Master" mode

It is possible to avoid these songs but they are prevalent in the "Dance Master Mode" option available in the main menu.

I like to use the Dance Master mode in which you have to unlock songs by doing well.

When I put it in my ps2, it STOPS when loading a song on either the Dance Master Mode AND the Free Play Mode

Instead of simply playing songs over and over again to unlock new ones, you need to clear different stages in the all-new Dance Master Mode.

So, I started playing and thought that the dance master mode is fun, even though it forced me to play some songs that I really, REALLY

Replacing Extreme US's Mission Mode, Dance Master Mode is loaded with several different scenarios with certain songs and a certain task to clear in order to advance to new stages.

Sure, Dance Master mode is fun, but I feel kinda ripped off

A fully fleshed out Dance Master Mode allows players to fulfill various mission objectives, earning points in order to purchase new songs, character costumes, challenge courses, and more