Lil Question on Atonement

Am pondering on the question on atonement.
I was reading a mandarin christian book on atonement and it strucked me that the writer explained that the crucifixion of Jesus Christ is not for everyone in the world but to the selected people who have been predestined to be saved even before the world being created.
All this while I have been believing that John3:16 'For God so loved the world, that he gave his only Son, that whoever believes in him should not perish but have eternal life' proves that Christ's death as atonement is for everyone in the world. However, I came to understand that this verse is actually continued by saying that the salvation is for those who believe. After understand a little bit more on the doctrine of predestination we came to understand more on God's authority. Christians have been called by name before the world began. Thus, it is logical that the atonement for sins is only meant for christians but not everyone. Our sins will be cleansed when God forgive our trespasses. If the atonement is for un-predestined human as well then it is useless for us to commit our sins as it will be forgiven regardless on whether we admit we are sinners or not!! sweat!!