Teabing's "study" is actually the ballroom, converted into a massive space filled with desks, books, and a surprising amount of technological gear.
Teabing proudly reveals an eight-foot long enlargement of the Last Supper, and proclaims that it shows the Holy Grail.
Sophie is confused. Didn't he just tell her the Holy Grail was a woman?
Yup: the person seated on Christ's right in the painting, if you look really closely, is indeed a woman.
Sir Teabing explains that our preconceived notions of the scene are so strong, no one ever notices that there's a chick in the midst of the disciples.
And she's not just any chick. She's Mary Magdalene.
Part of the smear campaign against women in the Bible is what maligned poor Mary.
She wasn't a prostitute (something that's implied pretty strongly in the Bible); she was Jesus's wife.
There are a bunch of small idiosyncrasies that support the theory that Da Vinci was painting the Holy Grail, like the fact that the space between Mary and Jesus's bodies creates a perfect "V", like the symbol for "chalice".
Even though the Bible says that Jesus was a confirmed bachelor, it's a matter of historical record that he definitely wasn't.
He was Jewish, for Pete's sake. According to custom he would've had to be married.
Teabing shows Sophie a book of the Gnostic Gospels, which clearly indicate that Jesus was married to Mary.
That makes her remember an angry priest coming to yell at her grandfather about an editorial he'd written regarding The Last Temptation of Christ.
Then Teabing shows Sophie the gospel of Mary Magdalene herself. It reveals that Peter was jealous of Mary, because she was the one that Jesus intended to carry on his church after his death.
(But. According to the Bible, Peter is the one Jesus instructed in his wishes. The plot thickens.)
It gets worse. Mary was of royal blood. Just like Jesus was. So their political union had the potential of a legitimate claim to the throne.
So. The "chalice that held the blood of Christ" is actually Mary Magdalene's womb.