Then your proof that all people are immortal because God is immortal fails.
The Bible says that evildoers are doomed to destruction. Obviously they are not immortal.
Though the wicked sprout like grass
and all evildoers flourish,
they are doomed to destruction forever;
Psalm 92:7 ESV
Do you agree or disagree that evildoers will be destroyed?
What do you mean by destroyed? Here are several verses which use שָׁמַד/shabad and which do not mean to annihilate, totally cease to exist.
Leviticus 26:30 And I will destroy [שָׁמַד/shabad] your high places, and cut down your images, and cast your carcases upon the carcases of your idols, and my soul shall abhor you.
Numbers 33:52 Then ye shall drive out all the inhabitants of the land from before you, and destroy [שָׁמַד/shabad] all their pictures, and destroy [שָׁמַד/shabad] all their molten images, and quite pluck down all their high places:
Deuteronomy 1:27 And ye murmured in your tents, and said, Because the LORD hated us, he hath brought us forth out of the land of Egypt, to deliver us into the hand of the Amorites, to destroy [שָׁמַד/shabad] us.
Deuteronomy 2:12 The Horims also dwelt in Seir beforetime; but the children of Esau succeeded them, when they had destroyed [שָׁמַד/shabad] them from before them, and dwelt in their stead; as Israel did unto the land of his possession, which the LORD gave unto them.
Deuteronomy 2:23 And the Avims which dwelt in Hazerim, even unto Azzah, the Caphtorims, which came forth out of Caphtor, destroyed [שָׁמַד/shabad] them, and dwelt in their stead.)
Deuteronomy 28:51 And he shall eat the fruit of thy cattle, and the fruit of thy land, until thou be destroyed [שָׁמַד/shabad]: which also shall not leave thee either corn, wine, or oil, or the increase of thy kine, or flocks of thy sheep, until he have destroyed [שָׁמַד/shabad] thee.
Deuteronomy 28:63 And it shall come to pass, that as the LORD rejoiced over you to do you good, and to multiply you; so the LORD will rejoice over you to destroy [שָׁמַד/shabad] you, and to bring you to nought; and ye shall be plucked from off the land whither thou goest to possess it.
Deuteronomy 33:27 The eternal God is thy refuge, and underneath are the everlasting arms: and he shall thrust out the enemy from before thee; and shall say, Destroy [שָׁמַד/shabad] them.
Joshua 7:12 Therefore the children of Israel could not stand before their enemies, but turned their backs before their enemies, because they were accursed: neither will I be with you any more, except ye destroy [שָׁמַד/shabad] the accursed from among you.
Joshua 9:24 And they answered Joshua, and said, Because it was certainly told thy servants, how that the LORD thy God commanded his servant Moses to give you all the land, and to destroy [שָׁמַד/shabad] all the inhabitants of the land from before you, therefore we were sore afraid of our lives because of you, and have done this thing.
Joshua 11:14 And all the spoil of these cities, and the cattle, the children of Israel took for a prey unto themselves; but every man they smote with the edge of the sword, until they had destroyed [שָׁמַד/shabad] them, neither left they any to breathe.