Why does extreme sexual dimorphism exist?

Have you read this segment of the Anglerfish article on Wikipedia?

Then let's pick a mandrill or any other animal where the male is more capable.

http://www.mnn.com/earth-matters/animals/blogs/9-most-dramatic-examples-sexual-dimorphism

Why do the males evolve by natural selection in ways that enhance survival of the species (such as muscular strength), while the females show no such evolutionary patterns. In fact, many of the ways that females evolve are in ways that attract males.

Why does it make sense for the mandrill species to have the male mandrill much more capable of surviving?

Survival and reproduction is what all animals and genders strive for.

Beauty, for example, is a reproductive tactic. Being able to attract males increases both survival and reproduction. For males, having stronger bones and muscles ensures that the male mandrill will be able to climb trees or avoid predators quicker.

But why wouldn't it make sense for the female to also be able to climb trees as effectively as a male?

Why must "beauty" be the females only survival tactic?

How does it make sense for the species to have one gender significantly weaker?

It's really hard to say. I mean maybe females are more attracted to males that are stronger than they are. Maybe it has to do with the different types of sex hormones produced by each gender. One contributing theory is Female-Choice (http://faculty.vassar.edu/suter/1websites/bejohns/mateselection/files/choice.htm) - basically that women had (or has) the ability to be more selective when it comes to choosing a mate. Over time men will reflect the preferences of women (taller than them, stronger than them, facial hair qualities, etc.). This is superficially supported by causal studies like this study from OkCupid where the "attractiveness" curve for men is down-shifted, meaning women think the average man looks below average in attractiveness and implying those who are viewed as average ( actually the top 20% of men or so) would have better reproductive success. Men, in the same causal study, had a nearly perfect bell-curve associated the attractiveness of women, implying that men are excellent at deducing whether a women is below average in attractiveness, average, or above average in attractiveness.

But the question was...

Why do males evolve in ways that serve a survival advantage to the species, such as large muscles and agility.

While females are selected to evolve traits that only serve to attract males, such as having a large ass, emitting sex pheromones, and female "beauty." This serves no survival advantage to the species other than attracting the male. The male is the one who actually allows the species to survive.

Males can survive without females. Females can't survive without males. The only things males can't do by themselves is reproduce. This is true in SOME species, but I think there are certain mammal species where the female takes the active role in hunting role, such as cats, but I'd have to check up on this.

Why wouldn't BOTH genders evolve in ways that help the species, and not just to attract mates.

I understand your question clearly, you're asking, why did nature choose a dominant gender in terms of strength. Why don't females produce the same amount of testosterone as males to be quick and strong? Why don't females look for "beauty"? Why is there a divide in how we see the world?

To be honest, i don't know, but I can speculate that perhaps this divide happened accidently/randomly sometime in our evolution because it doesn't happen everywhere in the animal kingdom. Basically men, at some point (and still might) compete with other men to win over women. The bigger, stronger man would presumably win in a fight and eliminate his competition - directly preventing the production of offspring by the weaker male. The male-male competition also holds true in a more speculative theory in that the winners of wars literally raped their way to reproductive success.

The first sexually reproducing organisms were hermaphrodites. These hermaphrodites split into two genders, one producing eggs and the other producing sperm. The gender that produced sperm required less energy to feed it's reproductive system. This allowed it to evolve (and compete with other males) in ways that enhanced the survival of the species (size, strength, agility, intelligence, etc.).

Perhaps ones these males took off, they gained a monopoly on these survival tasks and the egg-producing gender was simply not needed to do it.

But this still doesn't explain female-dominant species. I suppose their energy-intensive reproductive systems don't hinder them completely.

To be honest, I'm just trying to come up with a scientific argument against feminism and explain why human societies were always male dominant for almost 200,000 years until recently.