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Hebrew was the language in which the NT writings were originally produced, because it was the only language that the cohenim used.

It was the language of Matthew, the first NT author, and of Paul, the most prolific author.

Hebrew was the language in which the NT writings were originally produced, . . .

Prove it. That is, without using Roodian (il)logic.

I've no doubt whatsoever that Matthew and Paul were literate in Hebrew. I'm not aware that anyone has disputed this. The early Fathers of the Church attest to it.

Around 130 AD, Papias, bishop of Hieropolis in Asia Minor, wrote, "Matthew compiled the sayings [of the Lord] in the Aramaic language, and everyone translated them as well as he could." (Aramaic was very close to Hebrew.)

Around 180 AD, Irenaeus of Lyons wrote: "Matthew also issued a written Gospel among the Hebrews in their own dialect."

Although Paul was literate in Hebrew, most --- but not all --- scholars think his original autographs in Koine Greek.

But that wasn't the question. We were discussing whether Hebrew was the common spoken vernacular language of the 1st century Jewish people, the language Jesus spoke. It was not. Jesus' and His Jewish neighbors' spoken language was Aramaic.

By that time (the 1st Century) Hebrew was almost exclusively a written language. People outside of Jerusalem itself rarely or never used it conversationally.

As of the first century AD:

Jewish liturgical written language in Jerusalem: Hebrew.
Jewish daily conversational language throughout the Middle East: Aramaic.
Literary written language all over the Eastern Roman Empire (east of Italy): Greek.

Plus, an educated religious Jewish man who was also a commercial traveler and/or a Roman citizen (like Paul) would be reasonably adept in all three languages: Aramaic face-to-face with other Jews, spoken; Hebrew and Greek written. And probably he could manage in spoken Latin as well, like in his frequent dealings with the Roman authorities.

Paul was a highly gifted man.