The problem is that you're importing a modern English sense of "inspired" that doesn't match the Greek word Paul actually used.
In 2 Timothy 3:16 he says "All Scripture is theopneustos" (θεόπνευστος). It's a compound-adjective comprised of theos (God) and pneustos (breathed). It literally means "God-breathed."
That's why many translations (NIV, LSB, AMP, CJB, and others) render it "All Scripture is God-breathed" and the ESV similarly says "breathed out by God." The biblical claim isn't that the authors were influenced. It's that Scripture itself originates from God's own mouth — He breathed it out, so to speak.
If we're going to critique the doctrine of inspiration, we need to start with what the text actually says, rather than reading later English connotations back into it.