God Who shows no partiality, predestined all of Adam's race as His adopted children through Jesus (Eph 1:3-5), wrote all their names in the registry of heaven, the book of life, BUT only overcomers will not be blotted out from it (Rev 3:5).Wrong.
Scripture teaches predestination according to foreknowledge. 'Predetermination' is the Calvinist position you're disagreeing with.
Think of predestination like this, when you see a ship sail into the horizon, you cant see where it's destination is. But if you are lifted up, you can see beyond the horizon. Everybodys destination is hell without divine intervention to correct the course. It is God who intervenes according to foreknowledge, and alters the destination to a new course determined by God before the worlds were formed (Rom 8:29).
For as long as one's name remains written in the book of life, he is heaven-bound (Rev 21:27). And people are born with their names written in the book of life. Only Christ can blot out one's name from there. And He will do this for those who in their lifetime chose to be overcome of evil instead of overcoming evil with good (Rom 12:21; Rev 3:5).
The good news is there is hope while alive, because it is only AFTER a person dies that judgment is rendered (Heb 9:27) whether to blot his name or not from the book of life. God waits for man throughout his lifetime to become overcomers of evil.