Men and women, by virtue of their respective biologies, are not equal. Unless everyone is forced to undergo some surgical procedure in some future dystopia, "Equality of the Sexes" is an oxymoron.
The confusion arises when the argument behind the statement is implying political equality. Women have been, and in some cases, continue to be denied their Rights as individuals, and that is a matter that should always be addressed. Equality under the Law is what is really being called for by these slogans, and in that respect, Women and Men, as sovereign individuals exercising Rights, are and always should be equal.
Bessides physical and biological differences, I think that most differences between the sexes are based on cultural and societal experiences and expectations. If we removes society's biased expectations, I believe that we will find that there are no jobs that are better suited for one gender. Everything from morals, handling stress, memory, happiness, and so on really depends on the individual.
Women are capable of doing anything a man can do. There are differences of course such as men are generally physically stronger than women. I think the main thing that makes the capabilities of men and women the same is their mental ability. Men and women are equally smart. Women used to have specific roles that have been changing over time. Women used to generally stay home and do the cooking, cleaning, and raising the kids but this role has changed. Today, there are many women who hold the same jobs that men do.
Men and women have their obvious differences and one one gender group tries to take on a skill of the other gender group they might face challenges but it can be done. Look at women who join the military, they have to endure similar boot camp and have to prove to have similar skills in order to be apart of the military. I think society has a huge effect on what we think we can do as an individual based on our gender. Many people have proven to take on a "man's job" or "women's job" with no problem. Women are supposed to take care of the family and household, but there are many single fathers out there that can balance their work with the chores of homelife.
Both men and women are capable of great intellect and powers of deduction. While some will argue that women have trouble making decisions, there are women who are of high rank in the military and defense organizations such as the FBI, CIA, and the police which prove otherwise. Women also have great powers of observation an attention to detail which makes them good in detail-oriented professions such as crime investigation and medical fields.
While men are usually more physically strong, women are better at handling multiple jobs at once and handling stress. Women are also usually able to handle lack of sleep and pain better than men--childbirth is a great example. This is why they make excellent doctors, nurses, teachers, and attorneys.
Interestingly enough, I have read studies that "prove" that women are sick less often than men. So, maybe you could make an assumption that the immune system of women is generally stronger than men's?
There are perceived weaknesses in both genders, but the strengths of the other put them both on equal grounds. Hope this helps. I have no proof of any of this other than my powers of observation. You should search psychology experiments and papers written as a result for the proof you seek.
The most important aspect that makes men and women equal is their mental capacities. There are no differences in average mental capacities of men and women, and this is the most important asset or capability among human being.This equality of mental capacities is the main justification for considering men and women equal.
There are some clear difference in bodily dimensions of women and men. Women are on average smaller than men in terms of physical dimensions of their body. This also means that on average they have less physical strength. But in today world, physical strength is not very important, and therefore no justification for discriminating between men and women.