Parents of John Cary "The Plymouth Pilgrim"

There has been no proof of parentage for John Cary. I refer you to this website ==> http://www.advsolutions.com/carey/descendants.htm :

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 leaving his entire estate to his wife Grace in order to "tie and bind them [his children] the more to be loving and dutiful to their tender and careful mother". John Cary was an adult in 1633 and came to Plymouth the next year. Grace's will in 1668 leaves her son John, "if living" a shilling. That suggests that she and her son John were estranged. These circumstances roughly parallel the family tradition that John Cary came to Plymouth in 1634 following a dispute over his father's estate.