The Bible teaches that God has indeed predestined the saved to be saved. In Ephesians 1:4-6 we read:
"even as he chose us in him before the foundation of the world, that we should be holy and blameless before him. In love he predestined us for adoption as sons through Jesus Christ, according to the purpose of his will, to the praise of his glorious grace, with which he has blessed us in the Beloved." (ESV)
At the same time, we know from Scripture that God does not desire the death of the sinner, but that he should turn from his way and live (Ezekiel 18:23). We also know that God desires all to be saved and come to the knowledge of the truth (1 Timothy 2:4).
Now, we can do three things with this. We can go the Arminian route and maintain free will at the expense of God's election. We can go the Calvinist route and assume that God actually kinda wants the death of a sinner. Or we can hold these equally true passages of Scripture in tension. We can hold that God elects the saints from before the foundation of world, and that he does not elect people to damnation, but that they by their impenitence harden themselves, at least at first (see the example of Pharaoh). They seem logically incompatible, but then again, so does the doctrine of the Trinity. Theology need not fit a logical system. It merely needs to repeat back to God what He has said to us in Scripture.