Forget logic. God is beyond our understanding. The Church preceded the New Testament.
That seems to be pretty common malady amongst Catholics who fancy themselves some kind of intellectuals in spite of that.
►“Once he does so (joins the Catholic church), he has no further use for his reason. He enters the Church, an edifice illumined by the superior light of revelation and faith. He can leave reason like a lantern at the door.” (John H. Stapleton, Explanation of Catholic Morals, Chapter XIX, XXIII. the consistent believer (1904); Nihil Obstat. Remy Lafort, Censor Librorum. Imprimatur, John M. Farley, Archbishop of New York)