WAS ELIZABETH OF THE AARONIC LINE, OR THE DAVIDIC LINE?

Luke 1:5  There was in the days of Herod, the king of Judaea, a certain priest named Zacharias, of the course of Abia: and his wife was of the daughters of Aaron, and her name was Elisabeth. (KJV) Luke 1:36  (God speaking to Mary) And, behold, thy cousin Elisabeth, she hath also conceived a son in her old age: and this is the sixth month with her, who was called barren. (KJV)

Note: the assumption of contradiction is that the Bible establishes that Mary is of the line of David, but Elizabeth (who is Mary's cousin) is said to be of the line of Aaron. There are two possibilities here.  For one thing, all lineage is passed along the paternal line, so if Mary's mother and Elizabeth's mother were sisters (or, for that matter, if one's mother and one's father were brother and sister), they would be cousins yet would not necessarily be of the same lineage.  Also, the word for 'cousin' here (suggenes), according to Strong's, means 'a relative (by blood); by extension, a fellow countryman, kin'.  So they weren't necessarily cousins in the sense that we think of the term.  In fact, ONLY if Mary's father and Elizabeth's father were brothers would this be a contradiction.  Since that cannot be established, this is not a contradiction.