STUDENT 1: Damn, it's so crowded in here.
STUDENT 2: Open a window, miss, it's hot!
STUDENT 3: I can't move! Move your desk, I gotta get around!
ALL: There's too many kids in this class!
Class size is more than just the number of kids in a room. It's about, for one thing, the physical space required to increase class sizes. Classrooms are simply not built, in general, to accommodate 34 (0r, heaven help us, more) large young adults, plus computers and SmartBoards and classroom libraries. There's quite a bit more stuff in rooms than there were when many of our schools were built, and while much of the "stuff" is welcome, you can't stuff in more stuff and more kids and expect it to just work itself out. Kids are uncomfortable, easily distracted, and learning suffers.
As well, it's about the rigor of work and the amount of individualized attention you can give children in larger classes. You can't dramatically raise the rigor in a large class when many of those students will need a lot of support to meet those higher standards. You can raise the standards for, say, 15 high-needs kids and have a pretty good chance they'll be able to meet them; or you can have a class of 35 and accept the same mediocre work because you just can't give intensive support to those 15 kids while also trying to motivate and manage the other 20.
Finally, there are needs that we as teachers are expected to address that teachers in countries accustomed to large class sizes are not expected to address. Yes, you can have large class sizes if classes are full of mostly intrinsically motivated students and if the rest are under the firm control of high cultural expectations and administrations and families that back up these expectations. We simply don't have that here, and there doesn't seem to be much chance of building those expectations that would allow for large class sizes.
But go ahead, Mayor Bloomberg, raise those class sizes, fire those teachers...and get the same old results. Because maybe your so-called "legacy" as the "Education Mayor" hasn't been proven to be quite enough of a sham just yet.