No, no such thing as "bad" genetics. Just genetics and look at it from your own perspective and not measuring yourself in short comings compared to someone else. Do your best to be your best from the start, instead of going in with a negative feeling that someone is better.
A few things...
If you are speaking of BBing proportions many smaller guys look better than the larger counterparts just because of the builds or proportions.
It is also hard to tell how much actual muscle mass you can build onto whatever size bone or height you have.
My wrists are not 7" either, but I have managed over the years to hit 19" arms, and a reasonably fit looking #235 of BW.
Lots of guys are smaller, but strong as all **ck.
Lots of guys I know have small wrists, but big arms too.
Lastly, never never, never, never, never give up- Winston Churchill