The sinful nature is biblical because while the Bible does say we are new creations in Christ (see 2 Corinthians 5:17, Galatians 6:15) it does not say that our old nature is completely removed by our conversion to Christ. For instance, Galatians 5:13 says, “You, my brothers and sisters, were called to be free. But do not use your freedom to indulge the flesh; rather, serve one another humbly in love.” In this passage, Paul is claiming that it is possible for a Christian to “indulge the flesh.”
Flesh (sarx in Greek) is a word that Paul uses alternately with sinful nature. They are synonyms. Likewise, in Romans 8, Paul says we do not live by the flesh but by the Spirit. He says, “For if you live according to the flesh you will die; but if by the Spirit you put to death the misdeeds of the body, you will live.” (Romans 8:13)
How can you put something to death if it does not exist for you? It is my opinion that pretending we have no sinful nature does not actually help us to put that sinful nature to death. Realizing we have a sinful nature and a natural inclination to sin will help us to be aware when we are having that inclination so that we can put it to death. Anything less will leave us feeling discouraged or even questioning if we are even Christians just because we are still tempted to sin.
Putting to death the sinful nature takes time and constant effort while relying on God (Romans 12:1-2). While we initially put to death our sinful nature at our conversion to Christ (See Romans 6:1-4), we have a constant responsibility to put to death our sinful nature every day of our lives (Galatians 5:16, 25).