if Kate and Lilly have the same parents then why is Kate an alpha and Lilly an omega? Is it because Kate was born first?

I think it's based on the skills and abilities that they can do. Kate is a good hunter and she can fight, Lilly is shy and timid. Alphas are the stronger ones, Omegas are the weaker ones. This is just what I think.

I think, it's aptitude question.