We focus on the "red" words because God chose to send his only Son to reveal some of the scripture. Christ was not just another prophet or even a peer of Moses and the Apostles, he is one in being with the father. The words spoken by Him were as if received directly from the burning bush. Were the actual words of Christ no more important God could just as easily have given the entire revealed word by proxy.
The entirety of the Bible is God’s word, is Jesus’ word. To ignore, belittle, dismiss, or otherwise reduce any part of the word of God is a sin. Would the Ten Commandments be any less important if Paul had been the scribe?
He did...
Those aren't Jesus' words that He penned in the red ink...Those are the words of someone who 'claimed' he heard Jesus say those things...
Just as God spoke to prophets and they recorded God's words...If the words of God in the OT were in red, would you latch onto those words and ignore every thing else in the OT???
Most of my bibles don't have any red ink at all...