[EatsRainbows (OP)]

Males in many species perform for females, or fight one another for the rights to mate. This ensures the males with the best genes are selected for the future generations of individuals. But what about the females? Do ALL female individuals mate assuming they survive to mating age? Could it then be argued that strength of genes present in a species is the responsibility of males?

[mabsj2]

not all females reach reproductive maturity. most females that are "unfit" don't successfully mate. they die before reaching reproductive maturity or they simply don't get mates. that's how they are selected against.

[rosy]

I'll turn this question round... how would a female who was not "fit" (which is to say, reproductively successful) pass on her genes to the next generation? Any individual which either does not reach reproductive maturity (and find a mate and have offspring), or whose offspring do not themselves reach maturity, is by definition not "fit".
The whole notion of "fitness" is widely misunderstood. Fitness means no more and no less than reproductive success. What characteristics are required for success depend on the environment the individual finds itself in... and may change with time and place for a given species, but there's no way of determining what's "fit" without reference to what works.

[EatsRainbows (OP)]

I'm aware that all females may not reach reproductive maturity, but the same could apply to the males without all the competing and such but would not be such an effective mechanism for selecting the most ideal males out of all, therefore it seems the females challenges are 'weaker'.

I suppose maternal skills in rearing their young would play a part too in ability to pass on genes to future generations, however this would be a waste for the males on females that do not succeed to rear their young, and this is assuming it is the female that does do most of the rearing.