This week's book giveaway is in the OCAJP 8 forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide and have Edward Finegan & Robert Liguori on-line! See this thread for details.
As Paul tries to explain, even if you leave off the public access modifier, the compiler automatically assigns all interface methods to be public. This is specified in the Java Language Specification, so the real answer to your question about why we have to do it this way is: "Because Sun said so!"