The Catholic church teaches that we DO have a choice to say "Yes" or "No" to God's invite and that God has predestined no one to go to hell. (which is basically what the Bible says).  Some call this "pre-ordination" rather than pre-destination.

And yet the subject of predestination, even within the framework of Catholicism has intrigued theologians for centuries.  Look it up on the internet and you get a lot of hits - different theories on how it can exist in tandem with the free will God gave us.

The catechism doesn't say much about this except the following:

600 To God, all moments of time are present in their immediacy. When therefore he establishes his eternal plan of "predestination", he includes in it each person's free response to his grace: "In this city, in fact, both Herod and Pontius Pilate, with the Gentiles and the peoples of Israel, gathered together against your holy servant Jesus, whom you anointed, to do whatever your hand and your plan had predestined to take place." For the sake of accomplishing his plan of salvation, God permitted the acts that flowed from their blindness.

But it seems that an unequal amount of grace is bestowed on various humans and why this is, no one really knows....

Fr Mitch Pacwa, SJ has an interesting theory about this:

Some people are chosen by God to receive such graces that it is a certitude that they will be in Heaven. This is taught by the church. Not double pre-destination - which Calvin taught i.e. that human beings are so totally depraved that they do not have free will at all, not even to say "yes" to God's Grace so God pre-destined some to Heaven by giving them grace and making them take it and also predestined some to hell by not giving them the grace. People have no choice in the matter according to Calvin and thus this could be called "Double Predestination".

The Catholic church teaches that everybody has free will. We depend on God's grace to be saved but we also say "yes" to the grace and "No" to the grace.

God gives such amazing Graces to some people, that it is very difficult for them to say "No" - there is such delight in their lives and such an abundance of Grace that it is almost impossible for them to say "no" (although they still would be able to say "no" - they have the free will).

Why are those Graces given to people? The Special Graces are given to those people so that the rest of people who have ordinary grace can be lifted up by them, can be exhorted to come to God. God gives these people these graces not only for their sake but also for the rest of us, to inspire us and tell us about the beauty of God.

Fr Mitch Pacwa, S.J. "Threshold of Faith", EWTN
 

For sure what Jesus said is true "I came to give life and life abundantly" and each of us can increase the Grace we are given by seeking God, by praying, by going to Mass frequently and by doing the Will of the Father in loving others, caring for others for one thing which is agreed upon - we are totally dependent on God's Grace to bring us to Heaven.