You have all 12 half steps. Each can have two names=24. Then double it for minor makes 48.
You didn't think this through, did you. For the notes A, D, and G, what are your two names please?
By your logic, each note should have three names (not two) because in addition to the note's actual name, you can flat down to it from above or sharp up to it from below. For example the note A can also be called G## or Bbb. The note Bb can also be called A# or Cbb. Et cetera.
So by your (flawed) logic, there are actually 72 keys (since each of the 12 notes has 3 possible names, that's 36 major keys, then another 36 for the minor keys).
6 pages in and I still agree with Victor Wooten: By music-theory convention, double-sharps and double-flats are avoided in key signatures, giving us a total of 30 commonly-used keys (out of the infinite number of theoretical keys).
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