I suspect that what is confusing you is that you have encountered the phrase go to school only in contexts where go has its ordinary sense of “move from one place to another”, such as
I go to school by bicycle.
But American schoolchildren* rarely have occasion to use go to school in this sense. For most Americans going to school has a much broader sense.
The author contrasts go to school with live and work, which have similar senses here. Obviously you work at many places, including (I hope) at school and at home. Work here means “perform an economic role”. Equally obviously, you do not restrict your biological existence to your home; you live at work and at school, too, even if those don‘t seem like much of a life. Live here means “perform a domestic role”—there is an enormous popular literature on achieving “work/life balance”.
Similarly, go to school designates one of the major social roles: attending school, performing the role of student.
What is your occupation? ... I go to school.
Consequently, “a building to go to school in” is perfectly ordinary: it means a building where one performs school activities.
Study would not work at all in this context. Aside from the fact that American schools include many activities which have nothing to do with academics, the term is too narrow. For American schoolchildren intransitive study does not mean to engage in academic activities; it means to cease all other activities and concentrate, by yourself, on your schoolwork. In fact most US secondary schools designate distinct periods during the school day for just such studying; for historical reasons these periods are called study hall.
* The passage was clearly originally written for children: note the reference to “your father’s office”. The hypercorrective comma after And suggests a US origin to me.