Well yes, Jairus contradicted himself.... doesn't mean Bible is wrong.
Surely it's a simple case of Matthew contradicting Mark, not Jairus contradicting himself?
But the bible contradicts itself in many little ways eg
Mark 6:8 He charged them to take nothing for their journey except a staff; no bread, no bag, no money in their belts;
Matthew 10: 9 Take no gold, nor silver, nor copper in your belts, 10 no bag for your journey, nor two tunics, nor sandals, nor a staff;
And in big ways. Mark's Jesus is an ordinary Jew until God adopts him as [his] son on his baptism. He's not descended from David.
The Jesuses of Matthew and Luke are the products of divine insemination and have God's Y-chromosome. They're each descended from David by genealogies which are as fake as each other and completely irreconcilable (and Jesus is not the son of Joseph in those stories anyway).
The Jesuses of Paul and John pre-existed in Heaven with God, created the material universe (regardless of Genesis 1), and were born into Jewish families which are descended from David.
And that's just a tiny sample.
I think the problem arises because of a Christian tradition that the bible must be read so as to tell a single unified story. Since it very clearly doesn't, since it very clearly is written in separate books at separate times and places by separate authors (sometimes more than one author per book) with separate purposes and separate agendas, the tradition of a unified story is untenable when you read the documents impartially.
That doesn't prevent them from being valuable records of ancient thought, of course.