The sin of Adam corrupted all men's nature. It is very much a "thing"
You can call Adam's sin a thing if you wish.
You don't inherit Adam's sin, you "inherit" the consequences of Adam's sin. Specifically, your parents are unable to communicate to you sanctifying grace -- the indwelling life of the Blessed Trinity -- through the natural generation process.
Had Adam not sinned, they would have been able to do that.
There are other things that you inherit, but most of them are absences of things you should have inherited. Death is the absence of immortality. Concupiscence (tendency to sin) is the absence of the wisdom and strength of will to properly resist and understand sin. And so on.
Adam didn't "give" you anything. He squandered your inheritance. If your great-grandfather squanders your inheritance, does your father transmit poverty to you?
We inherit Adam's entire nature which is God-denying, God-fleeing.
Remember, God didn't put Adam and Eve's children back into the Garden of Eden for a second chance to see if they could do better.
Because they couldn't.
We all bear the disobedient nature of our first Father which can only be forgiven by Christ on the cross.
"But he was wounded for our transgressions, he was bruised for our iniquities: the chastisement of our peace was upon him; and with his stripes we are healed. " -- Isaiah 53:5
The fallen human nature that is passed from Adam to all men is not just an absence of good; it is a real propensity and desire for sin. And the only thing that cleanses our hearts of this is God's grace through faith in Jesus Christ.
"for whatsoever is not of faith is sin." -- Romans 14:23