Is that really what he said?
You probably should take everything in context, as taking things out of context very often leads to error. That, and this is why one should consult several versions and, for the most part, leave the KJV alone.
First, as I have posted elsewhere, we have this:
1Jn 1:8 If we say we have no sin, we deceive ourselves, and the truth is not in us.
1Jn 1:9 If we confess our sins, he is faithful and just to forgive us our sins and to cleanse us from all unrighteousness.
1Jn 1:10 If we say we have not sinned, we make him a liar, and his word is not in us.
1Jn 2:1 My little children, I am writing these things to you so that you may not sin. But if anyone does sin, we have an advocate with the Father, Jesus Christ the righteous.
1Jn 2:2 He is the propitiation for our sins, and not for ours only but also for the sins of the whole world. (ESV)
We see that from the very start of chapter 1 and continuing throughout, on past these verses, John uses first person plural pronouns--"we," "us," "our." He is clearly speaking about himself, the other apostles and disciples, and then including all believers.
Then, we see that those who think they are believers, those who include themselves in the "we," "us," and "our," but claim to be without sin are self-deceived, don't have the truth, make God a liar, and don't have his word in them. But, in between that, we see that by confessing our sins, God will forgive and cleanse us. This is then brought up again at the start of chapter 2.
In 2:1, we read "My little children," which does not describe unbelievers. His point there is clearly that if one of the "little children" (one of the believers to whom he is writing) sin, there is "someone who pleads with the Father on our behalf—Jesus Christ." More than that, in verse 2 he clearly differentiates between "our sins" and "the sins of the whole world."
We also have this:
1Jn 5:16 If anyone sees his brother committing a sin not leading to death, he shall ask, and God will give him life—to those who commit sins that do not lead to death. There is sin that leads to death; I do not say that one should pray for that. (ESV)
Which is an absolutely clear statement that believers do sin.
James affirms this as well:
Jas 5:13 Is anyone among you suffering? Let him pray. Is anyone cheerful? Let him sing praise.
Jas 5:14 Is anyone among you sick? Let him call for the elders of the church, and let them pray over him, anointing him with oil in the name of the Lord.
Jas 5:15 And the prayer of faith will save the one who is sick, and the Lord will raise him up. And if he has committed sins, he will be forgiven.
Jas 5:16 Therefore, confess your sins to one another and pray for one another, that you may be healed. The prayer of a righteous person has great power as it is working. (ESV)
No. It's because the whole Bible is full of man sinning, even the NT:
Gal 2:11 But when Cephas came to Antioch, I opposed him to his face, because he stood condemned.
Gal 2:12 For before certain men came from James, he was eating with the Gentiles; but when they came he drew back and separated himself, fearing the circumcision party.
Gal 2:13 And the rest of the Jews acted hypocritically along with him, so that even Barnabas was led astray by their hypocrisy.
Gal 2:14 But when I saw that their conduct was not in step with the truth of the gospel, I said to Cephas before them all, “If you, though a Jew, live like a Gentile and not like a Jew, how can you force the Gentiles to live like Jews?” (ESV)
Paul confronting Peter in his sin.
1Co 2:1 And I, when I came to you, brothers, did not come proclaiming to you the testimony of God with lofty speech or wisdom.
1Co 2:2 For I decided to know nothing among you except Jesus Christ and him crucified.
1Co 2:3 And I was with you in weakness and in fear and much trembling,
1Co 2:4 and my speech and my message were not in plausible words of wisdom, but in demonstration of the Spirit and of power,
1Co 2:5 so that your faith might not rest in the wisdom of men but in the power of God.
...
1Co 2:12 Now we have received not the spirit of the world, but the Spirit who is from God, that we might understand the things freely given us by God.
1Co 3:1 But I, brothers, could not address you as spiritual people, but as people of the flesh, as infants in Christ.
1Co 3:2 I fed you with milk, not solid food, for you were not ready for it. And even now you are not yet ready,
1Co 3:3 for you are still of the flesh. For while there is jealousy and strife among you, are you not of the flesh and behaving only in a human way? (ESV)
Paul considered the church at Corinth to be believers, who had received "the Spirit who is from God," but believers who clearly struggles with sin as they grow towards maturity and completeness in Christ.
Heb 4:14 Since then we have a great high priest who has passed through the heavens, Jesus, the Son of God, let us hold fast our confession.
Heb 4:15 For we do not have a high priest who is unable to sympathize with our weaknesses, but one who in every respect has been tempted as we are, yet without sin.
Heb 4:16 Let us then with confidence draw near to the throne of grace, that we may receive mercy and find grace to help in time of need. (ESV)
It is clearly stated that we, which is all believers, have weaknesses. Notice the clear implication--Jesus can "sympathize with our weaknesses" because he was "in every respect . . . tempted as we are," but was "without sin." It is because only Jesus was perfect that we can approach God with confidence to "receive mercy and find grace to help in time of need." That means we can overcome temptation, but that is only if, we do what is stated in verse 16.
Much of the NT deals with sin and tells us how we can overcome temptation so we don't sin. However, it is clear that we do still struggle with sin. To say otherwise is to make God a liar, which is blasphemy.