he did not mean anything of his quality etc.
Note by Henry Craik to letters 23 from Journal To Stella

Swift's meaning seems to be that the Duke of Shrewsbury made a handsome speech, in refusing to base any claim to observance for Buckingham on his quality; he meant to attribute Buckingham's refusal to make advances to his personal pride, in which a commoner might be equal with a duke, and Swift has now met their waiving of 'quality' by assuming that no man is to take his stand upon his personal pride. No man ever belied his own theory more.