How can a Christian be forgiven for sinning? I don't understand how this can be.

All that Christians have to do to be forgiven for sinning is to admit the wrong they have done and tell God they are sorry.
If we confess our sins, He is faithful and just to forgive us our sins and to cleanse us from all unrighteousness. If we say that we have not sinned, we make Him a liar, and His word is not in us.

My little children, these things I write to you, that you may not sin. And if anyone sins, we have an Advocate with the Father, Jesus Christ the righteous. And He Himself is the propitiation for our sins, and not for ours only but also for the whole world.
(1 John 1:9-10, 2:1-2 NKJ)
When we repent and confess our sins, God is faithful and just to forgive us our sins. God will even cleanse our souls from any unrighteousness that sin might have caused.

God desires for us to come to the place where we avoid continuously falling into sin and then repenting; but as often as we do sin, we can repent and God will forgive us. This is all part of the benefits of Jesus' death on the cross and the shedding of His blood for us.

This particular benefit is not just for Christians, but for the entire world. The world, or those who are not Christians, receive forgiveness for their sins when they accept Jesus as their Savior (John 3:16-17) and become Christians. Once they're in the family, then they can use the same Scriptural process to stay clean (1 John 1:9-10).

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