FW being against the predestination doctrine predates his conflict with Fritz, and indeed predates Fritz’ existence. To summ up a longer tale, Tiny Terror FW was an unruly kid terrorizing his teachers until Mom and Dad gave him a really strict Calvinist teacher (despite being lax believers themselves). Thereafter, FW was a strict Calvinist living in religious terror especially due to the predestination doctrine, and argued himself into thinking in this particular case, Luther was right, not Calvin. But it continued to trouble him throughout his life and kept coming up.

Ergo: Fritz could have found no surer way to strike at Dad under the guise of submission (since he was reading religious books and talking with the preacher, as demanded) than to declare himself a believer in predestination. Aside from that, it also was a way to justify himself. (I.e. assert his individuality - if God had meant him to be the way he was, etc.). But seriously, Predestination was a life long terror to FW, and anyone who knew him personally knew that.