There is controversy on who John's father was. The following information is provided by David Carey: Matawadave@aol.com 
"The parents of John Cary, the Plymouth Pilgrim, have yet to be positively 
identified. Most theories have been disproved. He was not the son of John 
Cary and Elizabeth Hereford. Their son John was married in 1613 (when the 
Pilgrim was about 3 years old) and died in Hackney , Middlesex, England, 
before 1665. Proof is found in the pedigree submitted by their grandson John 
Cary, the famous London and Virginia merchant, to the Earl Marshall of 
England which resulted in confirmation of his right to bear the arms of the 
noble Carys of Devon (ref. College of Arms, Book of Grants IV) Copies of 
those documents are filed in the British Library (Stowe MS 670, folio 229) 
and in the Society of Genealogists Library, London.

John the Pilgrim was not the son of Elizabeth and William Cary who was 
mayor of Bristol in 1621. That theory was proposed by Henry Grosvenor Cary 
in his The Cary Family in America and is disproved by the Heralds College 
pedigree of the Bristol Carys. The son of Elizabeth and William Cary was the 
John Cary who married Elizabeth Hereford (see above).

The theory that John the Pilgrim was the son of Walter Cary and Grace 
Browne has not been disproved or proved positively. Walter died in 1633, 
about the time the Pilgrim came to Plymouth after a dispute over his father's 
will. Grace left a will in 1668 naming her son John "if living", which 
indicates that he was estranged from her as the Pilgrim was from his family.

David Carey" 

.. 2 Thomas Cary b: December 1613 d: 1659

. +Susanna Limberry