I never understood why until I spoke to a teacher from one of the schools. Most parents fight the closure to prevent having to put their kids on buses or having to drive them to school that is further away. They are also short-timers, or rather, their kids are short-timers. Their kids are only in that elementary school for a few more years and don't think about future kids who plan on attending. 

Another big reason why parents fight to keep schools open are due to the teachers and administrators. If you close a school, those teachers are and admin staff will be out of a job. So they're motivated to communicate to students and parents on how "bad" closing the schools will be for those students/parents, when they're really just looking out for themselves.

 It’s the students who suffer the most from this type of behavior. 

My children aren't yet in school, but I do have some observations living in a district where this issue arose.  The school board was considering closing one of the elementary schools in the area and most of the parents I spoke with were incensed b/c the district had a lot of other areas where they could reduce costs and the closure of this school wasn't the only option.  There were allegations that administrators were using district funds to purchase private luxury items under the pretense of a school related item (ie: big screen tv, other electronics).  You also have the added concern that a community will ultimately be split up and people always want to avoid that.