Definition of secure computation with more that two parties
It is not enough to be able to simulate the view of a single party, because corrupted parties may cooperate. As mentioned in the book, it may be easier to view all the corrupted parties as a single entity. It is the view of this single entity that we must simulate.

If $m$ is fixed, the order of quantifiers does not matter, because the number of subsets $I$ is fixed and so a single simulator $S$ can of course incorporate the code of the simulator $S_I$ for each $I$ (since $S$ is given $I$, it knows which of the $S_I$ to run as a subroutine).

(Edited after a comment.) If $m$ is not fixed, this may not be possible (for example if $m$ grows polynomially with the security parameter, the number of subsets grows exponentially), so you get two possibly different definitions depending on the order of the quantifiers. The one with a single simulator is stronger (if there is a single simulator that can generate a valid view, there trivially is a family of simulators that can, but not the other way around), so it is the one that was used. In practice, no protocol is known which is secure for the first definition and not the second.