[liuhenry]

The ELI15 explanation is that at these temperatures, quantum mechanical effects take over and the atoms themselves become indistinguishable from each other. They no longer have a definite position in space and experimentally act as matter waves [1].

This diagram is for bosons, but the top two boxes still apply for fermions (Bose-Einstein condensates are different but closely related): https://condensed-matters-cmcdt.wp.st-andrews.ac.uk/2019/02/...

The process is 1) cool until the de Broglie wavelength is larger than the typical interparticle distance and 2) compress.

If you did 2) before getting 1) then you would risk forming a classical liquid/solid. More info on the process: [2].

[1] https://en.wikipedia.org/wiki/Matter_wave [2] https://www.uni-muenster.de/Physik.AP/Demokritov/en/Forschen...