The first one is the why question of being born again. The how is answered here:
Mark 10:17-31 17 Now as He was going out on the road, one came running, knelt before Him, and asked Him, "Good Teacher, what shall I do that I may inherit eternal life?" 18 So Jesus said to him, "Why do you call Me good? No one is good but One, that is, God. 19 You know the commandments: 'Do not commit adultery,' 'Do not murder,' 'Do not steal,' 'Do not bear false witness,' 'Do not defraud,' 'Honor your father and your mother.' " F46 20 And he answered and said to Him, "Teacher, all these things I have kept from my youth." 21 Then Jesus, looking at him, loved him, and said to him, "One thing you lack: Go your way, sell whatever you have and give to the poor, and you will have treasure in heaven; and come, take up the cross, and follow Me."
Being born again is the first step of repentance -- shunning evils as sins. Which evils? Those set forth in the Ten Commandments. As I stated, all religions follow the Ten Commandments and indeed the commandments extend outside religion to civil law. Christian Conservatives fight to keep the Ten Commandments in the town square today.
As I said, being born again is a process. It does have a first iteration when a person decides to freely shun evil when he otherwise would not and then proceeds into the repentance process I described earlier. Note that this is not unique to Christianity.
If you have lived your life well, you have gone through the process of regeneration.
The next verse adds more context to the 2nd quote:
10 If we say that we have not sinned, we make Him a liar, and His word is not in us.
We are to confess our sins individually as the Catholics do, not wholesale like the reformed. I won't get into the whole forgiveness thing because we don't believe in 'original sin'. We believe in hereditary sin which is passed from parent to child, grandparent to parent, throughout the ancestors which are treated differently than sins of our own making.
Therefore, we do not believe in vicarious atonement.
According to John 3, being born again is a one time event accomplished by The Holy Spirit, e.g. spiritual regeneration. Paul in Romans indicated we are "raised to walk in newness of life". Being born again is a singualr event that occurs when one repents and trusts in Jesus to forgive and save them based on his sacraficial death. John, Chapter 1 states:
12. But as many as received him, to them gave he power to become the sons of God, even to them that believe on his name: 13. Which were born, not of blood, nor of the will of the flesh, nor of the will of man, but of God.
Being born again is of God, not of us!
Your quote of Mark 10 left out the rest of the story, when the disciples exclaimed, based on Jesus' impossible requirements:
26. And they were astonished out of measure, saying among themselves, Who then can be saved? 27And Jesus looking upon them saith, With men it is impossible, but not with God: for with God all things are possible.
So again, the salvation event is of God alone, not based on our works!!!
As I stated, all religions follow the Ten Commandments
Really? Many religions (some Christian) pray to idols, and few observe the Sabbath (including most Christians), and most don't acknowledge the YHWH of the Bible as the one, true God. Hindus, for example, believe in a multiplicity of God;s.