I am not sure why this is such a controversial statement in this day and age. There are obvious biological differences and we are often so busy trying to deny them that it hurts people.
This issue has a lot of facets.
Firstly, yes, there are biological differences between men and women. However, the extent of those biological differences has come into question. Scientifically, we're beginning to appreciate more and more that the way in which biological human sexuality influences the skills, behaviors, and abilities of is not easily understood or abstracted. As we become more advanced, our understanding of the sexes becomes increasingly complex. It contradicts the black and white model we developed in the past.
We come from a day and age where it was believed that men and women were, essentially, wildly different from one another.
The gender roles of the past have been heavily dramatized because they were based on the fundamental belief that males and females are opposites, and, also, not equal. That philosophy stems mainly from religion and the patriarchy. As a consequence of these fundamental beliefs, as mass manufacturing dominated the market, and materialism really started to take hold, toys and clothes for boys and girls became increasingly gender-dramatized.
There's a couple of ways to observe this cultural evolution. Some of the best, in my opinion, are to check out the evolution of fashion, toys, and the differences between marketing generations (like Generation X, and Millennials). In fashion, Marilyn Monroe used to be the standard of beauty. That standard was soon replaced by models like Twiggy (an androgynous supermodel), and Gia Carangi (a supermodel of the Heroin Chic movement). Even today, androgyny and Heroin Chic are still influencing our standards of beauty. On the male side of things, you had body builders like Arnold Schwarzneggar. These extreme standards for male and female beauty soon became the "status quo" through media marketing. The irony is that many of these people were not necessarily attractive in person (unlike Marilyn Monroe), but it was their unrealistic and extreme appearance that made them stand out, and therefore made them more marketable, which is really how the "supermodel" was made.
When you look at the way toys and clothes for kids evolved, you'll notice that not that long ago, it was common to dress young male and female children similarly. Children also generally played with the same toys. It wasn't until children started to get slightly older, and their hormones started to influence their biological structure, that they were increasingly treated according to their gender role. However, after mass marketing and materialism really took hold in our culture, we started dressing boys and girls in overly-gendered clothing and grooming them with our speech and behaviors at a much earlier age...and in a very unrealistic way. Dressing girl children like princesses and boy children like superheroes, for instance. Boys played video games and legos, and girls played with barbie dolls and easy bake ovens.
To wrap this all up, if you look at our recent history, you notice a trend. Genderization becoming increasingly extreme. Gender roles becoming increasingly black and white, and more importantly, increasingly unrealistic and unattainable. Eventually, this led to a sort of "era" in US television and media where the female sex was increasingly regarded as stupid, weak, and incompetent. So much so, that it became a bit of an infamous running joke in male-orientated advertisements. There's a lot of jokes, for instance, about how women can't drive, or about how women might burn the house down because they're too dumb to use an appliance properly. Playing dumb became attractive. The "ideal woman" started to become one that was highly superficial, extremely ditsy and uneducated, sickeningly people-pleasing, and illogical.
Eventually, technology outstripped the role of the "homemaker". With TV dinners and vacuums, and other things that made it easier to manage house and home, the role of the mother became increasingly undervalued and unappreciated, and women began adopted more and more jobs outside of the home. As a consequence, there was no longer an invisible wall between the genders, and men and women had to develop more of a mutual respect and ability to work together than had ever been required of them before.
On the male side of things, traits that traditionally defined the male sex, like strength, slowly became outdated and unnecessary due to the evolution of our technology. At this point, the advantages males have due to sexual dimorphism are no longer necessary for survival, and in many cases, can be disadvantageous to thriving in modern society. I think this might be one reason why males may be becoming increasingly less masculine. Masculinity is just not necessary in the same way as it used to be.
So that brings us to where we are today. Males and females are now having to work together in ways that, historically, we never really had to, and our culture, patriarchy, and understanding of gender norms is still struggling to evolve to accommodate that chance. Additionally, we've evolved beyond the necessity of masculine traits - strength, aggression, and so forth. So now, not only are these traits less valued and less sought after, and our male beauty standards have become much more feminine, but they are often viewed as disadvantageous because many of the negative aspects of testosterone are more relevant now, than ever, due to the male/female workforce integration.
So, to answer your question...you asked why we're not allowed to talk about gender differences. My answer to that, in my personal opinion, is that people aren't ready to "go there" right now, because our culture is in a period of rapid, quite uncomfortable change. Women are extremely sensitive these days about their recent historical gender roles and the way their sex has been regarded by men (as stupid, weak, and essentially useless for everything except making sandwiches and birthing babies). Conversely, men are extremely sensitive to what they see (quite accurately) as an attack on their personal masculinity, and on "what it means to be a man" (the male gender role). There is a massive male struggle at the moment between modernized men and those still beholding to traditional male stereotypes. Everyone is on edge, and everyone is defensive. Sexism is ridiculously rampant. People are frustrated enough to strangle one another.
Times are changing. Every time, throughout history, whenever humans have been forced to rapidly change their culture, it's been very stressful. Some people adapt quickly, others take a very long time, and some will hold on to traditional gender norms until their dying breath. These disparate opinions cause a great deal of strife.
Someday in the not too distant future, the outdated mindset will die off, and what you will be left with is a culture where men are far less masculine and women feel far more secure in their gender. When we learn to be less sexist is and racist, we'll return to issues regarding the biological differences between males and females, and various races. We'll have to, if we're to make scientific advancements in medicine. Much of western medicine was made exclusively off of studies of white males. I seriously doubt that the liberal agenda to silence this kind of distinction will actually play out in the long run. It's just a symptom of the underlying cultural issue at the moment.
