The Watchtower Society's stance against university is grounded in its historical roots.
During the late 1800s and early 1900s, home study courses that were designed to focus on specific trades and bodies of knowledge were developed by the International Correspondence School. These home study courses were promoted as being beneficial because they did not include any other knowledge than that which was applicable to one particular trade.
At about the same time that Thomas Foster was developing ICS' home study courses, Charles Russell published and sold his Home Bible Study course.
Two early cohorts of Russell, Clayton Woodworth and George Fisher, were heavily involved in the ICS. They were both textbook writers for ICS at the time that they wrote The Finished Mystery.
Clayton J.Woodworth did much of the writing for The Golden Age magazine and the correspondence school influence is apparent in some of the articles. For example, the Feb. 18, 1920 issue of The Golden Age (pg 339) has an article on the bee keeping industry and at one point in the article the author gives a plug for correspondence schools:
Mail order courses in beekeeping are also to be had for the benefits of those unable to attend college
The anti-university stance of the WTS has been around since its inception.