Superstring theory doesn't "presume" the existence of six more dimensions. The number of dimensions rather "falls out of" superstring theory. So, it is more like the other way around. See this answer to a question of mine on Physics SE.
So there are several reasons to believe that d=10 within the framework of superstring theory. The [...] explanations are not independent of each other of course. You can simply pick whichever is your favourite and use that as your explanation for d=10.
Also see these questions on Physics SE: 1, 2, 3, and Why String Theory?: a layman's journey to the frontiers of physics and Number of dimensions.
There are also criticism and proposed alternatives (many, presumably, with different numbers of dimensions) to string theory. I cannot judge whether such criticism holds (any or most) water, but it seems at least partially inspired by ideas in philosophy of science/physics.
There seem to be opposing camps, with a lot of mud-throwing between them. To me, it appears that these camps hold different attitudes to what the philosophy of final theories should be. See also Theory of everything (philosophy).
So, in conclusion, there are people picking fights about candidate physical theories, and for a layman like me it is difficult to even judge whether these fights are constructive in some sense, but they are (presumably) not directly about certain ideas about or attitudes towards the number of dimensions, but rather indirectly.