It is a negotiated number informed by science, not a threshold found in the physics, and both halves of that matter.
The 2 degree figure came first, in policy discussions from the 1990s onwards. 1.5 entered through the Paris Agreement in 2015, pushed hard by small island states for whom the difference between 1.5 and 2 is existential rather than incremental.
The IPCC special report in 2018 then examined that difference rather than inventing it, and found it was substantial: roughly twice the species losing half their range, and coral reefs going from severe decline to near total loss.
So the number is a political choice about acceptable risk, resting on a real and measurable difference between two futures.