What do you do when you find someone in your family behaving badly and bringing the family name into disrepute? There are two main strategies: either you can try and reason with them to bring them round and restore your shared reputation, or you can leave the family, change your name and hope that the bad publicity stays at a distance.

Tony Campolo has decided to follow the second strategy. He has announced that he "did not want to be known as an evangelical Christian any more". In doing this, he appears to have two kinds of concerns. The first is reputational: the term has too many negative connotations, especially among non-Christians. But Campolo also feels that evangelicals in the United States are simply not being true to the teaching of Jesus:

"Evangelicals in the United States are anti-environment... If you say you're an evangelical you're anti-gay, you're anti-women, you're pro-war...In the southern states, 80 per cent of the people go to church at least once a month [and yet it's] the strongest supporter for capital punishment.

"How do you reconcile evangelicals favouring capital punishment when Jesus said: 'blessed are the merciful'?"

But is Campolo's decision going to achieve what he wants? Campolo wants to focus on the teaching of Jesus, not least through his participation in the 'Red Letter Christian' movement which focuses on Jesus' words in the Gospels. But in dispensing with the label 'evangelical' he appears to be contradicting his own convictions. Evangelicals (broadly speaking) see the Scriptures, and particularly the teachings of the New Testament, as the decisive authority for life and faith. This is in contrast to liberals, who (broadly speaking) look to reason and experience to determine belief, and Catholics who (broadly speaking) look to the teaching ministry of the Church to determine what they should believe.

So if might be that if Campolo is simply shedding the label, he isn't achieving very much. If his concern is that US evangelicals (and others) are not following the teaching of Jesus, then his concern is not that they are being too evangelical – but that they are not being evangelical enough. And by putting distance between himself and their views, he is actually throwing away any hope of engagement and debate. Surely a more fruitful strategy would be to agree that the New Testament needs to shape us – and take the discussion from there?

I doubt that ditching the label is really going to help the PR either. I wonder how much difference it makes to non-Christians for us to say to them "Oh, I'm not a horrible Christian like those miserable evangelicals! No, I am a nice kind of Christian – you can trust me!" I am not sure that those outside the Christian faith find it quite so easy to draw these neat lines – and I am pretty sure that God doesn't. We might like to carve ourselves up into different groups, traditions and denominations; I have a suspicion that such divisions are ones that God doesn't take too much notice of.

I wonder how far Campolo's strategy for reading the New Testament will get him anyway? So called 'Red Letter Christians' focus on Jesus' teaching, and Campolo thinks that focusing on Jesus' teaching will enable us to focus on mercy and love. He is quite right that Jesus' emphasises non-violence in personal relationships and that it is very hard to justify the kind of nationalist militarism (often based on American Exceptionalism and the myth of redemptive violence) that is found in many parts of the Bible belt. But the Jesus who said "Turn the other cheek" (Matthew 5:39) also said that those who don't believe will be "thrown into the blazing furnace, where there will be weeping and gnashing of teeth" (Matthew 13:42). The one who was "gentle and humble in spirit" (Matthew 11:29) also thought that those who mislead "little ones" (those who are vulnerable in the faith) should have "a large millstone were hung around their neck' and should be 'drowned in the depths of the sea" (Matthew 18:6). If we want our Jesus meek and mild, then we are going to have to cut out a lot more than the black letters.

And here's the heart of the difficulty: if we start cutting down our Bibles to remove the awkward bits, or the bits that we think others are interpreting wrongly, there is no knowing where it will take us. Steve Chalke is quite clear: the writers of parts of the Old Testament were mistaken in their description of God, since it doesn't match with his notion of the loving Jesus he follows. But in fact, Luke also makes the same mistakes, in writing about Ananias and Sapphira in Acts 5. So perhaps Luke is also wrong in writing down some of Jesus' own teaching that we find difficult? It turns out rather quickly that we have stopped following Jesus, and starting asking Jesus to follow us. When we separate the Jesus of history from the Christ of faith, then we are worshipping a god of our own creation. The Bible calls that idolatry, and has some fairly strong things to say about it.

Focusing on the red letters actually undermines historic Christian belief. Many of the non-canonical writings, such as the Gnostic Gospel of Thomas, are collections of Jesus' teaching, and some of them aren't too far away from Jesus' teaching in the canonical Gospels. But that is only one part of the good news, and misses out on the most important. Jesus didn't simply come to be a wise teacher and enlighten us with spiritual knowledge; he came to do something for us that we could not do – to be a "ransom for many" (Mark 10:45) by "dying for our sins, according to the Scriptures" (1 Corinthians 15:3). That means that the red letters actually don't make sense without the black letters around them – and that neither makes complete sense without that long introduction that Christians call the Old Testament, which is what Paul is referring to when he talks of "the Scriptures". The consistent mark of authentic early Christian teaching was that it understood all that God had done through Jesus as a fulfilment of what God had done before among his people Israel.

To be evangelical means to see the Bible, rightly interpreted, as the supreme authority in matters of life and faith. If my fellow evangelicals are giving the family a bad name by their misreading, then I need to stay in the family and have the conversation. And, guess what? There are some red letters about that:

"If a brother or sister sins, go and point out the fault, just between the two of you. If they listen to you, you have won them over" (Matthew 18:15).

Rev Dr Ian Paul is a member of the Archbishops' Council, and blogs at www.psephizo.com