The foundational premise is that Ever HaYarden possesses a lesser degree of holiness than Eretz Yisrael proper — the Ramban (Bamidbar 21:21) cites the teaching of Chazal that Ever HaYarden is not fit for the Beit HaMikdash or the dwelling of the Shechinah, and the Shem MiShmuel (Matot 8:7) elaborates that this lesser sanctity stems from the fact that it was conquered before Eretz Yisrael itself.
the Or HaChaim (Bamidbar 32:7) makes explicit that Moshe's actual preference was for all of Israel to dwell in the land that God gave them precisely because it would be more holy — meaning Moshe was keenly aware of the kedushah advantage of Eretz Yisrael proper.
Yet the Shem MiShmuel (Matot 8) explains why Moshe ultimately acquiesced: once the condition was set that Reuven and Gad would fight alongside their brothers before receiving their territory, Moshe understood that the land of Ever HaYarden would effectively be sanctified through its allocation following the conquest and settlement of the western land — and, faced with the practical reality that they needed cities for their children and enclosures for their flocks and would not build while the land was not yet theirs, Moshe was compelled to agree rather than enter into ongoing dispute.