I have enough money to put 50% down on my new house. Why would I want to only put 20% down?

You would only want to do this if you believe you can invest the additional 30% and earn a return greater than the interest rate on your mortgage. With interest rates at a historical low, borrowing money is cheap right now; but savings rates are even lower and the stock market is very volitile. A wise investor can make this work to his/her advantage, but just be careful!