your post and all the other posts here assume that there is some means for the mother deer to tell if she has a weakling in the oven or not, and then also has means to choose to miscarry weaklings.
Here's a less complicated hypothesis that has the same effect: Human's and chimps share >99% of their DNA. But an X and a Y chromosome are largely different. A human male baby is more similar to a male chimp than to his own mother. Whereas a human female baby is more simillar to her mother than a female chimp.
there is thus a much stronger possibility of a male fetus having a negative immune reaction to antigens from the mother. Normally a healthy mother and a healthy fetus can tolerate some mismatch. If the male is more robust or perhaps simply more developed early in the development process then the probability of tolerating the mismatch is higher than for a less developed/less robust fetus.
This is a simpler and more intrnsic mechanism that should be common across mammals.