Why are female not competitive for reproduction like males?
As @Dexter said, there are examples of species where female compete for the access to the males but most often it is the other way around; males compete for the access to the females.

The reason for this discrepancy is mainly explained by Bateman's principle. Citing wikipedia:


  Bateman's principle suggests that in most species, variability in reproductive success, or "reproductive variance," is greater in males than in females. This is ultimately a consequent of anisogamy. Females, especially mammalian females, almost always invest more energy into producing offspring than males invest. Bateman's principle anticipated and is consistent with Robert Trivers's theory of Parental investment—in most species females are a limiting factor over which males will compete. This competition results in some males being more successful than others, leading to greater reproductive variance among males than females