While the established paradigm of human evolution asserts that the lineages leading to the extant great apes and Homo arose in Africa, the large number of fossil discoveries from Europe in recent decades support arguments for a European origin of the Hominidae (all great apes) and plausibly, also a European common ancestor of the Homininae (African great apes, Australopithecus species, and the genus Homo). Meanwhile, a lack of consensus remains regarding the phylogenetic placement of australopithecine fossil species in Africa, with substantial evidence indicating that some of them may align more closely to extant African great apes than to Homo. Based on a novel interpretation of existing fossil, genetic, paleogeographic and paleoclimatic evidence, this paper aims to put forward a new hypothesis regarding the separate divergences of Gorilla, Pan, and Homo. We support existing arguments that the last common ancestor of African great apes and Homo may have lived in Europe in the late Miocene, and we put forward a new hypothesis as to where, when, and why the separate lineages may have started to diverge. Extreme conditions during the Vallesian Crisis (11.6-8.0 Ma) and the Messinian Salinity Crisis (6.0-5.3 Ma) may have forced separate branches of European hominids to migrate out of the Mediterranean region. We argue that the lineages leading to Gorilla and Pan independently migrated into Africa, while the lineage leading to Homo went in another direction. Thereafter, the Zanclean Megaflood (5.3 Ma)--which caused the Mediterranean to refill very quickly--may have cut off the migration route between Eurasia and Africa at the Sinai Peninsula, isolating a small population (the putative Homo lineage) on the Arabian Peninsula / Red Sea coast during a period of hyperaridity. The other group (Pan lineage) crossed into Africa, where it subsequently diversified into various species of Australopithecus.