The dispute over predestination is not about whether the New Testament uses the language of election, which it does, but about what follows from it for human freedom.
Augustine arrived at his position arguing against Pelagius in the early fifth century. Pelagius held that human beings can choose the good by nature and that grace assists rather than creates the choice; Augustine held that the fall left the will genuinely unable to turn to God, so that any turning must be produced by grace, and that God's choice of whom to save is therefore prior to and independent of anything foreseen in the person. Why some and not others, he declined to explain, calling it a judgement inscrutable but not unjust. The councils of the fifth and sixth centuries endorsed Augustine against Pelagius and against a milder position that made the first movement toward God human, without endorsing every implication he drew.
Calvin followed Augustine and pressed the logic. If God elects some, he necessarily passes over the rest, and Calvin was willing to call this reprobation and to say it is decreed. The doctrine is stated in the Institutes with a note that it is a dreadful decree, which Calvin regarded as no reason to deny it, and its function in his theology is pastoral as much as speculative: salvation is entirely outside the believer's control and therefore entirely secure.
Arminius, teaching at Leiden a generation after Calvin's death, accepted the corruption of the will and the necessity of grace but argued that God gives prevenient grace to all, restoring the capacity to respond, and that election is God's decree to save those he foresees will believe. This preserves genuine contingency in the human response while denying that anyone saves themselves. His followers, the Remonstrants, set out five articles in 1610.