As you may know, BTC transactions can be traced, and you have to verify your identity on pretty much all exchanges these days. So, if you withdraw BTC from the exchange to your wallet, there is a connection between your name and said wallet. From there on, the coins can be sent to other wallets or exchanges, and it is pretty easy to trace them further. Mixers make this impossible by mixing the coins of users and allowing them to withdraw coins to wallets and still remain anonymous. Basically, you can trace the withdrawal to the mixer. From there on, no one knows which coins are yours, especially if you split them into a smaller group. Think of that image of a ray of light entering the prism and exiting as a rainbow — only one or two colors are your money, but there is no way of telling which ones.