Double predestination is a synonym for election and reprobation. Both are controversial, but reprobation is more controversial. That’s because reprobation is really the acid test of one’s commitment to election.
Reprobation is simply the flip side of election. There are two lines of evidence for reprobation: direct and indirect:
1.Direct evidence in support of double predestination or reprobation comes from such verses of Scripture as Isa 6:9; Mal 1:2-3; Mt 11:25-26; Lk 2:34; Jn 3:19; 9:39; 12:39-40; Rom 9:11-13,17-22; 11:7; 1 Thes 5:9, 2 Thes 2:11; 1 Pet 2:6-8, and Jude 4.
2.Indirect evidence in support of double predestination or reprobation comes from the fact that reprobation is the logical corollary of election: if everyone will not be saved, and those that are to be saved are saved because God chose to save them, then the lost are damned because God chose not to save them, but rather, to reject them and condemn them.
As Geerhardus Vos puts it: “No more is necessary than to combine the two single truths, that all saving grace, inclusive of faith, is a supernatural gift of God, and that not all men are made recipients of this gift, to perceive immediately that the ultimate reason why some are saved and others passed by can lie in God alone.”
BTW, there’s nothing wrong with drawing inferences from Scripture. Jesus often castigated the religious establishment for failing to ponder the implicit teaching of Scripture. Both Paul and the author of Hebrews draw inferences from OT narrative theology.
In some circles, the phrase “double predestination” is contested. This goes back, in part, to a dispute between Berkouwer and Van Til. Both come out of the Dutch-Reformed tradition. However, Berkouwer, unlike Van Til, defected from Calvinism in mid-career.
There’s a partial asymmetry between election and reprobation. Election is unconditional in the sense that it does not take human merit or demerit into account. By contrast, reprobation has a conditional aspect inasmuch as God condemns sinners. This is not a sufficient condition of reprobation, otherwise everyone would be damned. Hence, reprobation remains a sovereign deed. Nevertheless, demerit is a necessary condition of reprobation. But both election and reprobate are determinate for the fate of the elect and the reprobate.