What's wrong with this code, part 3

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This time, let’s consider the following routine used to determine if two strings are equal (case insensitively).  The code’s written in C# if it’s not obvious.

            static bool CompareStrings(String string1, String string2)
{
//
// Quick check to see if the strings length is different. If the length is different, they are different.
//
if (string1.Length != string2.Length)
{
return false;
}

                  //
// Since we're going to be doing a case insensitive comparison, let's upper case the strings.
//
string upperString1 = string1.ToUpper();
string upperString2 = string2.ToUpper();
//
// And now walk through the strings comparing the characters to see if they match.
//
for (int i = 0 ; i < string1.Length ; i += 1)
{
if (upperString1[i] != upperString2[i])
{
return false;
}
}
return true;
}

Yes, the code is less efficient than it could be, but there’s a far more fundamental issue with the code.  Your challenge is to determine what is incorrect about the code.

Answers (and of course kudos to those who found the issues) tomorrow.