Why must the human body be kept at a pH level of 6.5 to 7.5?

The above answer from "nofret" is correct.  I wanted to add that the structure of enzymes makes it useful, and changes in pH unravel enzyme structure.  These changes in structure are referred to as "denaturing" the protein.  You can denature a protein (enzyme) by changing the pH or raising the temperature.  This is why we can cook foods with both temperature and acids (pickling).

Think of a screwdriver. Its shape makes it useful for putting in screws, where a saw's structure makes it useful for cutting.  Raising the body's pH is equivalent to breaking the tip off of your screwdriver.  Now, it cannot perform its function.

As to why the human body has particular pH levels, the enzymes have evolved in our body to function at these optimal levels.  By keeping body pH fairly constant, these enzymes are able to be specific in their function.