It is hard to know how to answer this question. My answer would depend on where the person who believes this is coming from. Is this someone who knows very little of the Bible? Is it someone who read a book or an article or who has heard multiple sermons teaching this false doctrine? Is it none of the above, for example a mature Christian who reached this as a possible conclusion on their own? In each case, I would resopnd differently.
Historically, this doctrine was first taught (as far as I know) by Pelagius, a monk and influential Christian teacher in the early fifth century. He was teaching in a context in which the church had become extremely worldly. Very few of the Christians, percentage wise, lived a righteous Christian life. Because many thousands came into the church after Constantine with little if any Christian conviction, the church had become very corrupt. Pelagius was counteracting this tragic trend by teaching the Christians ought to be able to approach perfection through being transformed by God. I believe that Pelagius was sincere, but that, in trying to right a wrong, he went too far. Pelagius argued that it is possible for us to become sinless after sufficient time, then we ought to do this. You can see how he applied this as a practical teaching on order to call the semi-pagan, unconverted people in the churches to change and to act like a Christian. However, his solution, like I said, was not a good one. Bottom line, the Bible teaches that we cannot become perfect during this life. The passage I would use would be 1 John 1:8. "If we claim to be without sin, we deceive ourselves and the truth is not in us. If we confess our sins, he is faithful and just and will forgive us our sins and purify us from all unrighteousness."
Many other passages could be used to prove that it is not possible for us to completely stop sinning while in this life, and the approach I would take, like I already said, would depend on the person who believes this. I hope this will get you started.