Why does this subtraction not equal zero?
This is because decimal numbers that "look" round in base 10, are not exactly representable in base 2 (which is what computers use to represent floating point numbers). Please see the article What Every Computer Scientist Should Know About Floating-Point Arithmetic for a detailed explanation of this problem and workarounds.
Floating-point inaccuracies (there are an infinite number of real numbers and only a finite number of 32- or 64-bit numbers to represent them with).
If you can't handle tiny errors, you should use BigDecimal instead.