ANSWER: The belief in predestination you are asking about is such a wonderful topic to study in the Bible! Christian denominations have been built, or broken, on misunderstanding this Romans 8 doctrine. John Calvin, one of the founders of modern-day Calvinism, is arguably the most well known proponent of predestination (although it was first formulated by Augustine, who lived from 354 to 430 A.D.). John's father wanted him to study law. If he had listened to his dad we may not have had all the chaos and confusion this teaching has caused Christians and the Christian world in general!
One popular dictionary states that predestination teaches that the final salvation of some people is ordained from eternity by God (Collins English Dictionary). Calvinism itself defines this teaching as the "eternal decree" of a perfect God who has, based on his will, already foreordained the eternal destiny (i.e. heaven or hell) of each human being before they are even born. We need, however, to think about the ramifications of believing in predestination.
You could be the saintliest person on earth, yet despite all your goodness, you could end up in eternal torment. Another person, on the other hand, could be the worst sinner on earth, yet because God foreordained him he could spend eternity in paradise. We may as well live a life of hedonism because it will not make one bit of difference in the end, if the false teaching of predestination is correct, since God has already determined whom the "winners" and "losers" are!
The primary Scriptural verse used to justify predestination is in the Apostle Paul's epistle to the Romans, chapter 8. It states the following, "Because those whom He did foreknow, He also predestinated to be conformed to the image of His own Son . . . " (Romans 8:29, HBFV throughout). What do these controversial verses in Romans 8 REALLY mean? David Brollier tells us the following.
"He (God) knew our sinful nature would preclude that (conforming to Christ's image), so he extended his grace to all who would accept the sacrifice of his son for our sins. His goal was that we would be exactly like his son in holiness and purity, but knew that without his power reigning in us it could never happen."
Note that predestination does not just affect certain people but ALL mankind. What Paul is teaching does not concern salvation per se, but God's desire that we be conformed to his son, Jesus Christ. The book of Ephesians tells us he planned, from the moment he determined to create the earth, that man would populate it, and no other beings but mankind should become his children (Ephesians 1:3 - 4). We are also told in the Bible that it was foreordained (a type of predestination in the sense that the Eternal decided in advance what he, not we, will do) that those who believe and obey the eternal God should be adopted by Jesus himself, through whom we have an inheritance according to his will (verse 11).
In the final analysis, what the word of God says about predestination has nothing to do with our future predetermined by our Creator. Our future is dependent on our decisions in life. As John Didymus Pope said, if God already has determined in advance just one person to die forever we would have to get rid of John 3:16, which is "For God so loved the world that He gave His only begotten Son, so that everyone who believes in Him may not perish, but may have everlasting life."