It comes down to this:
The first few levels of a class tend to be very "good", as that establishes the character and the class. Multiclassing allows a character to get these early levels (and the juicy abilities they bestow) multiple times. So multiclassing tends to favor optimizers.
Because of multiclassing's mere existence, it also puts a constraint on what can be offered to a 1st-2nd level class, as you add "too much" and its makes multi-classing even stronger.
So it puts a design constraint on the game, which some people do not like.