No, it’s not a central tenet. It was invented by Augustine who struggled with his own very sinful past. He found an excuse, a nature he couldn’t help.
The Bible says that God saw that “the intention of man’s heart is evil from his youth” (not before.) It’s also intention, not deeds. It’s not inborn, but it develops. Sorry but the foundation of christianity is forgiveness of sins actually committed.
The Bible says a lot of things, and making a doctrine out of one verse is big error.
Psa 51:5 Behold, I was brought forth in iniquity, and in sin did my mother conceive me.
Psa 58:3 The wicked are estranged from the womb; they go astray from birth, speaking lies.
Jer 17:9 The heart is deceitful above all things, and desperately sick; who can understand it?
Rom 3:23 for all have sinned and fall short of the glory of God,
Rom 5:12 Therefore, just as sin came into the world through one man, and death through sin, and so death spread to all men because all sinned—
Rom 7:18 For I know that nothing good dwells in me, that is, in my flesh. For I have the desire to do what is right, but not the ability to carry it out.
Rom 7:19 For I do not do the good I want, but the evil I do not want is what I keep on doing.
Rom 7:20 Now if I do what I do not want, it is no longer I who do it, but sin that dwells within me.
Rom 7:21 So I find it to be a law that when I want to do right, evil lies close at hand.
Rom 7:22 For I delight in the law of God, in my inner being,
Rom 7:23 but I see in my members another law waging war against the law of my mind and making me captive to the law of sin that dwells in my members.
Rom 7:24 Wretched man that I am! Who will deliver me from this body of death?
Rom 7:25 Thanks be to God through Jesus Christ our Lord! So then, I myself serve the law of God with my mind, but with my flesh I serve the law of sin.
Rom 8:3 For God has done what the law, weakened by the flesh, could not do. By sending his own Son in the likeness of sinful flesh and for sin, he condemned sin in the flesh,
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Rom 8:7 For the mind that is set on the flesh is hostile to God, for it does not submit to God's law; indeed, it cannot.
Rom 8:8 Those who are in the flesh cannot please God.
Rom 8:9 You, however, are not in the flesh but in the Spirit, if in fact the Spirit of God dwells in you. Anyone who does not have the Spirit of Christ does not belong to him.
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Rom 8:12 So then, brothers, we are debtors, not to the flesh, to live according to the flesh.
Rom 8:13 For if you live according to the flesh you will die, but if by the Spirit you put to death the deeds of the body, you will live.
2Pe 2:18 For, speaking loud boasts of folly, they entice by sensual passions of the flesh those who are barely escaping from those who live in error.
Why do people sin? Because their flesh, their nature, is sinful. The big problem with your position is that it leaves open the possibility that people can live sinless lives just like Christ. That would, of course, be utterly false and heretical. Why do you think all people sin, as the Bible says? Why do you think even very young children don't need to be taught to hit other children or take toys away, etc.? We cannot not sin because it is in our nature to do so.
That we have a sinful nature is the only biblical position. Anything else leads is based on misunderstanding Scripture and leads to serious error.