"They have in their bishops an unbroken lineage going back to St Peter and his apostolic bretheren."
How can that be if they are celibate? And the Catholic Church itself wasn't established until after Peter's death and Peter was married BTW.
It is not a familial succession. It is passed down in the ordination - "laying on of hands" that transmits the charism (gift of the Holy Spirit) that make a man a priest.
Spiritual lineage. Read Paul on marriage and serving God.