"Kateřina has shorter hair than her son."
Translation:Kateřina má kratší vlasy než její syn.
In this case, why wouldn't 'svůj' be the correct possessive adjective? Katerina appears to be the subject (ona má) and possessor (její syn).
as a rule, reflexive possessives do not occur in the nominative. we can't have "Kateřina a svůj syn". the moment "svůj" shows up in the nominative case, it is as if self-possession were taking place, so it would mean "Kateřina and his own son". how it relates to the given sentence: in this case než is followed by the nominative case. you can see that from the zero ending of "syn" and from the completion of the comparison Kateřina má kratší vlasy, než má její syn. in which "její syn" is itself a subject.