Because of the requirement to print the number if it is divisible by neither. Here:

    if x isDivisibleBy 3: print "Fizz"
    if x isDivisibleBy 5: print "Buzz"

and.. how do I now print x in the neither case? I can't 'else'. I could make a long if not divisible by either if expression, but that's less easy to read than an if/else chain that starts out with 'if divisible by both, print fizzbuzz'.

If fizzbuzz was: Print FizzBuzz for multiples of 15, fizz for multiples of 3, and buzz for multiples of 5, and nothing otherwise, I bet you'd see the above pseudocode far more.