The word epitope was coined by Niels Kaj Jerne in 1960. He defined the term as:
"surface configurations, single determinants, structural themes,
immunogenic elements, haptenic groups, antigenic patterns, specific
(Aalberse RC, Crameri R. "IgE‐binding epitopes: a reappraisal". Allergy 2011; 66: 1261–1274.)
It is the place on the surface of the antigen where the antibody binds, so the word epitope is appropriate for that purpose, considering that epi (ἐπι) means upon or on, and topos (τόπος) means place.
Jerne also coined the term paratope, which is commonly thought of as the complementary place on the antibody that binds to the epitope. Because of a structural similarity, the paratope has an affinity for the epitope and naturally goes with it. I'm trying to emphasize the idea of with (and complement), because para (παρα) means with or beside in Greek. So, again, the word paratope is appropriate.
You also asked why it couldn't go the other way, i.e., why couldn't the epitope have been called the peritope and vice versa.
I suppose it could have been. The place on the surface of the antibody could have been called the epitope, and since complementarity is a mutual relationship, it could have gone the other way when designating the paratope.
However, when distinguishing between the elements of a mutual relationship, it's normal to choose one of them to serve as a reference, even if the choice is somewhat arbitrary. Besides that, it seems natural to choose the epitope as a reference, thus giving it priority. An analogy would be the way we speak of the pilot and copilot of a plane — one gets priority, and the other gets designated with a prefix which means with.