Squire graduated B.A. at Balliol College in 1560, and became a Fellow that year, graduating M.A. in 1564.[4] He became vicar of
Cumnor in 1568, and accumulated other preferments, being canon of
St Paul's Cathedral in 1577.[5]
Squire's suspicions of
Robert Persons were instrumental in forcing Persons, who was Dean of Balliol College, to resign his fellowship in 1574. They had clashed when Persons was Senior Bursar in 1572–73. Squire had an ally among the Fellows in
Christopher Bagshaw.[6]
Squire himself had a reputation for dealings with the supernatural. It was alleged against him by Persons that he sold
familiar spirits, in the form of a fly, to gamblers; or, in the term "dycing flies", the word fly was then a synonym for familiar.[7][8] The charge came close to losing Squire his post as Master.[9]Richard Harvey, in defending his own practice of
astrology, mentioned Squire among other academics as sympathetic to it.[10] According to Balliofergus he was "a great Mathematician".[11]
Squire embezzled a legacy given to the college.[12] Around 1580 he was paid off by the Jesuit
George Gilbert to turn a blind eye to the development of a Catholic association of young men in the area (
Farringdon Without) of
Chancery Lane or
Fetter Lane.[13] In 1588, the year of the
Spanish Armada, and also his death, he was given custody of a leading
recusant, Walter Fowler.[14]
John Strype relates that Squire preached his own wedding sermon, that he was unfaithful to his wife, and that Squire fabricated an affair she was having. Finding out about this, his father-in-law the bishop "cudgelled" him. Further, he ran up debts, and his estate was put into administration. John Squire was brought up by
Theophilus Aylmer, son of the bishop.[19]