Queen Side Castling

Today I was playing a game of chess on a board with my dad. We came to a point where I wanted to castle on the queen side in a similar position to this one. My father said I was unable to since the rook moved through the attacked square b8, however I thought that since the King wasn't moving through an attacked square, I could. What rule says one of us is right?

You can castle.

This king should not move through an attacked square and must not end up in check.

So here, both conditions are satisfied! 

I know of this incident where Victor Korchnoi asked the arbiter to clarify the situation: in the Candidates Final Match versus Karpov in 1974 in Game 21,  Korchnoi desired to castle at move 18 and was indeed able to do so.  However, it was not actually queenside castling.

Here is another incident; this one actually does involve queenside castling.  Yuri Averbakh objected to his opponent's castling move 14...0-0-0.  Averbakh's objection was dismissed.

Luke Lizard,

I’m sorry, you’re wrong. You lose by forfeit. 

There's a well-known type of trap that involves crossing an attacked square with the Rook: