Why do I need this Callback function in order to work properly?

Answer 1

The callback is called after the animation (changing opacity value) is done.

So if you remove the callback and append it directly after the animate, it will remove the classes before the animation is done.

Else if you remove the callback completely, you lost the way to remove the classes (of course XD")

Answer 2

That callback is removing the classes from the previously active slide ($active).

$next becomes the new active slide (and gets the class from the statement just prior to animate).

If the code didn't remove the class from $active there would be two active slides after all is said and done.