Who is the liar but he who denies that Jesus is the Christ? This is the Antichrist, he who denies the Father and the Son.

 More likely the explanation is this. When John says I am writing he is thinking of what he is at the moment writing and of what he still has to say; when he says I have written he is thinking of what has already been written and his readers have already read. The sense would then be that the whole letter, the part already written, the part being written and the part still to come, is all designed to remind Christians of who and whose they are and of what has been done for them. 