And the Lord God formed man of the dust of the ground and breathed into his nostrils the breath of life; and man became a living being.

The word "being" is translated from the Hebrew word "nephesh" which implies air breathing fleshly creature. See also Gen 7:22

The words immortal soul never appear in the Bible, nor immortality of the soul.

1 Tim 6:16 tells us that God alone has immortality.

Ezekiel 18:4 tells us that the soul that sins shall die.

Ecclesiastes 9:5 ...the dead know nothing

Matthew 10.28 But rather fear Him who is able to destroy both soul and body in hell (Gr. Gehenna).

None of these scriptures imply that man has an immortal soul, and with careful study, other passages that seem to imply that false teaching also fall in line with these scriptures.

When read in context, the Bible doesn't contradict itself.

Genesis 2:7