There is a short answer to this question - you are born with it.
Everyone inherits two copies of each gene (one from each parent). In Alpha 1-Antitrypsin Deficiency the genes you inherited are faulty. You do not produce enough Alpha 1-Anittrypsin. You might produce some Alpha 1-Antitrypsin and it may just sit in the liver! This can cause liver failure as well.
There are varying degrees of severity of the deficiency - so depending on which exact gene you inherit, you may get very sick, or you may not even notice that there is anything wrong with you at all.
For more information on how inheritance of Alpha 1-Antitrypsin Deficiency works you can check out these websites:
Genetics Home Reference: Alpha-1 antitrypsin deficiency
Genetics of Alpha-1 Antitrypsin Deficiency
For more information about genetics and inheritance in general you can check out this website:
Basics of Genetics
