Maybe Carl Svensson didn't want his kids to have to go all the way to Edestad for school, so he offered to have a new school built on his own land.
You may have a point there, although he probably wasn't alone, since the parish assembly (local farmers) were willing to approve the lease. I found some information that the school in Binga was a small one, for the youngest children (7-9 years). After that they had to go to Edestad. I even found a photo of it: http://diginpast.se/bb/peggy/index.html