Way, way back in ancient Roman time, there were hinges, which were called cardos. If something belonged to the hinge it was cardinis. The word was of great metaphorical use as the centre-point around which things turned, for example the celestial poles. So the central and most important priests, those who elected the Pope, were called cardinalis ecclesiae Romanae: etymologically hinges of the church of Rome.
Catherine of Aragon told Cardinals Wolsey and Campeius:
The more shame for ye: holy men I thought ye,
Upon my soul, two reverend cardinal virtues;
(Recorded by Shakespeare and Fletcher in Henry VIII)
But there isn’t really a connection, only a common ancestor. Religious cardinals do not, or should not, commit cardinal sins. Nor did they decide which sins would be named after them. Cardinal sins are so-called because they are the central sins, on which all the other minor sins depend. They are the sinful hinges.
So for example, the central cardinal sin of lust might result in your committing the particular sin of animal husbandry. Wrath might lead to murder, or violence, or simply taking the Lord’s name in vain.
Pope Paul VI may have had this in mind when, in 1974, he made Jaime Sin a cardinal, thus creating Cardinal Sin. Jaime himself liked the joke and referred to his official residence as the House of Sin.
One of the many idiots who have tried to prove that Shakespeare didn’t write Shakespeare, was a chap called Georg Cantor. He was a mathematician and invented set theory. He also coined the term cardinal numbers. As with the sins, cardinal numbers are the proper numbers (one, two, three, four) on which the ordinal numbers (first, second, third, fourth) depend.
So now you have it, spread the word.