I think a better reasoning is that NaN does not have a single binary representation but in software, one may not be able to distinguish them.

An f32-NaN has 22 bits that can have any value, originally intended to encode error information or other user data. Also, there are two kinds of NaNs: queit NaN (qNaN) and signalling NaNs (sNaN) which behave differently when used in calculations (sNaNs may throw exceptions).

Without looking at the bits, all you can see is NaN, so it makes sense to not equal them in general. Otherwise, some NaN === NaN and some NaN !== NaN, which would be even more confusing.