It is the Word that is infallible, not the mortal men who God has used to preserve His Word. Peter himself made gross errors, Jesus said he was directed by Satan, Paul rebuked him to his face. (No, I do not subscibe to the belief that Peter was the first pope).
I will not be drawn into the sophistry that the Word being infallible necessitates the (sometimes self appointed) guardians of the Word themselves be infallible. God is infallible, His Word is infallible - and He is fully able to keep His Word.
He used Balaam’s ass to accomplish His will; He is certainly able to use fallible men to preserve His Word.
It is God who is preserving the scriptures and His church.
You supplied a correct response, while only silence from those who support what is denied by Scripture.