I'm not sure why this was downvoted, it's a legitimate question.
The problem is the sheer quantity of transactions that occur on the various exchanges. Adding that volume to the public chain would make the public chain significantly larger than it is. The bitcoin.cc wiki Scalability page [1] does a better job of documenting the constraints than I could in this space.
The flip side of this is that there's a required level of trust when doing business with an exchange. Thus far no exchanges that I know of are actually publishing their ledgers - so we really have no way to know that all trades are made in good faith and all funds are properly managed by the exchanges.
Unlike regulated government currencies, there are no audit requirements. This means there is nothing that actually requires an exchange to be operating in good faith. I'm actually surprised that there are not yet any private exchanges[2] with public/open ledgers, in response to Mt Gox and various other scams (both for bitcoin and other currencies). Seems the market has to be there for it, after people have been burned so many times.
[1] https://en.bitcoin.it/wiki/Scalability
[2] that I know of. I know there are protocols under development intended to handle this, but no actual exchanges that simply publish all transactions for the world to see.
[edit] can't believe I used 'shear' instead of 'sheer'.
Yep. Look what happens every time a bitcoin bank folds. Everyone who had coins in that bank rather than in their own wallet suddenly loses every coin they have.
Bitcoiners strike a balance with on-chain and off-chain transactions because Bitcoin has several properties which make it undesirable for many sorts of transactions. A short list would include 20~60+ minutes for transaction capture, lack of a way for merchants to initiate transactions (the dominant method in B2C commerce in the US), user-unfriendliness of much of the ecosystemic software, etc.
Does this come with risk? Shouldn't all transactions be on the chain?