In Chapter 3, Victor recalls the day he left to attend the University of Ingolstadt and mentions why Henry Clerval does not go with him. Victor says that Henry attempted to persuade his father to let him enroll in the University of Ingolstadt but was unsuccessful. According to Victor, Henry's father was a narrow-minded trader who felt that his son would become lazy if he went off to school. Before leaving for the University of Ingolstadt, Victor recalls the firm look in Henry's eye that revealed his resolve not to become a trader like his father. In Chapter 5, Henry surprises Victor at school. Henry tells Victor that he finally convinced his father to allow him to enroll in the University of Ingolstadt. After constantly preaching about the value of education to his father, Henry gets his father to concede. He permits his son to attend the University of Ingolstadt alongside Victor. 

Victor has attended local schools, but when he turns seventeen, his parents want him to pursue further studies at the University of Ingolstadt. Their aim is to offer him an opportunity to interact with different customs and a new environment. His departure is delayed by his mother’s illness and subsequent death. 

Henry Clerval, Victor’s close friend, also wants to attend the same university. Henry tries in vain to persuade his father to allow him to pursue his higher education alongside his friend at Ingolstadt. Henry’s father is a trader and wants his son to pursue the same occupation. Thus he does not see the need for his son to pursue higher education. However, in their farewell meeting, Victor can tell that Henry remains resolute and determined to achieve his aspirations.

You can find the answer to this near the start of Chapter 3.  In that chapter, Victor is talking about how he is going to start school at the University of Ingolstadt.  Henry Clerval cannot come with him to school because Henry's father does not want him to go to a university.

We are told that Henry's father thinks that college makes people lazy.  Victor says that Mr. Clerval is narrow minded and only wants his son to focus on making money.  So Henry is not allowed to go off to the university with Victor.