Whitetail deer have 70 chromosomes, 35 from the male, and 35 from the female. So, no, the female cannot pass on more chromosomes, that it possess, which would be 42 chromosomes (60% of 70), that would go against the law laws of nature, read a book. I do think he has poor genetics, bases on his age. I don't cast my judgment solely based on his lame left antler, but more so on his small right. I don't think he will make it another year, he is getting very old, and is gonna get his fat butt pushed around come the rut, so why not take him out now. You've been served.