I believe the choice of the core size is twofold.
As from K8NVH good answer a minimum impedance is needed for the balun to do its job.
A common mode impedance much higher than differtial ones involved makes sure the balanced to/from unbalanced convertion takes place.
This somehow drives the size of the core for its mechanical dimensions shall allow the ...
When making a coax choke balun, does the size of the ferrite matter, and if so, why?
Simplest answer: If the choke impedance is low enough to allow some common mode power through, then there is a possibility of overheating. The bigger cores either dissipate heat better or provide higher impedance.
Another way to say the same thing: As long as the choke ...
SPICE modeling shows that replacing T2 and R with a 22.2-$\Omega$ resistor, the impedance looking into T1 is indeed 50-$\Omega$, as expected:
Similarly, replacing the 50-$\Omega$ generator and T1 with a 25-$\Omega$ generator shows that the impedance looking into T2 is 25-$\Omega$:
This is a result of the electrical symmetry about a "virtual ground" ...