She came from a religious family and disputed theological matters with her brother Thomas Parker.
He was removed by his bishop in 1607 after publishing his views that certain religious ideas were anti-Christian; for example, he stated the sign of the cross should be avoided.
[1] Avery published Scripture-prophecies opened, which are to be accomplished in these last times, which do attend the second coming of Christ, concerning theology and prophesy, in 1647.
He published his objections to her ideas in The copy of a letter written by Thomas Parker, pastor of the church of Newbury in New England, to his sister, Mrs Elizabeth Avery in 1650.
He admitted that he had not read her 1647 publication when he wrote "your printing of a book beyond the custom of your sex, doth rankly smell".