Here is a snippet out of W. Tong's biography of Matthew Henry, written soon after his death in 1716. He explains why Matthew Henry did not go to a university:
Mr. Phillip Henry had so great a kindness for the universities and valued so much the mighty advantages of improvement there, that he advised his friends who designed their children for scholars to send them thither for many many years after the change; but long experience altered his mind and he chose rather to keep his own son at home with him, than to venture him into the snares and temptations of the university.
And certainly in that way of education that his father chose for him, he not only escaped the snares of the publick universities, but made advances in all useful learning, equal to most that have been trained up in those famous nurseries of science; which yet must be imputed to as uncommon capacity and diligence, and to that blessing of God that always attended him.
An Account of the Life and Death of the late Reverend Mr. Matthew Henry, Minister of the Gospel at Hackney, who died June 22nd 1714 in the 52nd year of his age, 1716, P26.