How is Jason an Aaronide priest?

My family discovered a few years back that our Jewish background was actually a male-line "literal descendant of Aaron" background. We are no longer Jews in the traditional sense, but we are still Aaronide men and have the obligation to be proper priests of the Lord Jehovah, as were Aaron and his sons.

You doubt me?  Here is my evidence:

My 2nd Great-granduncle Lazar Nemrow's headstone is here and one can plainly see the carved symbol of the Kohen lineage at the top. His father was named "Isaac haKohen (the priest)" and Lazar's brother Joseph, who abandoned his Jewish faith to be more successful in America, was my 2nd great-grandfather.

Although Jewish-ness is passed through mothers, the Kohen priestly ancestry is passed from father to son.  Here is my direct male-line ancestry, to Isaac Nemrow the priest:
Now, I am not unique at all in my family's male line ancestry.  My father David has two brothers, who have several sons and grandsons between them, and I have one brother who has sons and grandsons, just as I do. However, to our knowledge, the men I mention here are the only present-day male-line descendants of Isaac Nemrow, who bears the "haKohen" designation.  Although our family is no longer Jewish by tradition, we are traditionally among Aaron's sons that bear the God's priesthood by lineage.

Interesting, huh?