In a world without generic programming, NaN not being equal to itself makes a certain amount of sense for some kinds of numeric code. But in a world with reusable generic algorithms the calculation changes -- here equality/ordering relations really must be transitive or weird shit happens. In C++ it's undefined behavior to call `std::sort` or `std::unique` on list of floats containing NaN.

Most languages nowadays have standard-library functions/types that require well-behaved equality, so why have a builtin type for which equality is not well-behaved?