If we could answer your question, we would be able to predict the future direction of science. But science is full of surprises. Moreover, what gets called "science" (or math or logic) and what gets called "philosophy" is to some degree arbitrary. I don't think disciplinary boundaries are very important. What I do think is important is the questions themselves. So why not ask the questions and not worry about whether they are "science" or "philosophy"?
or for another kind of response, you might still ask why many/most philosophers don't publish philosophies of life. You'd have to do an empirical survey there, but i'm guessing that for many, a philosophy of life is too big and hard to construct. Much easier to focus on some relatively narrow problem and work out a sophisticated view on it ... And I bet that professionally the incentive is to do the same. A "philosophy of life" is something that aims to the wider market, the general public, but the professional incentive is to impress the professional philosophers rather than the public. (Alternatively, perhaps many professional philosophers feel pretty confident that the main value in life, at least for them, is the very professing of philosophy -- so they are acting out their philosophy of life even without publishing their philosophy of life ....)
You ask an interesting question. If Philosophy was nothing more than deductive logic, then someone with skills in deductive logic but developmental issues elsewhere would probably excel in philosophy. But most people think that Philosophy involves more than deductive logic--it involves the exercise of "good judgment" which in fact we do not understand very well. Good judgment may or may not be absent of emotion: the philosopher David Hume puts emotion front and center in his ethical theories.
We have a very poor understanding of autism spectrum disorders (indeed the diagnostic category of Asperger's has recently been removed from the DSM). It used to be thought that people with autism lacked emotion; that is generally speaking not true (although the emotions may be different from those of neurotypicals).
On rereading your question, perhaps you see a correspondence between some philosophers' apparent detachment and some autistic behavior. There may be an overlap here but I doubt that it goes very deep (that is, I doubt that a shortcut to doing philosophy is to have your autistic friend do it).
Anyone and everyone can become a philosopher by asking questions about knowledge, existence and ethics. Being a philosopher is like being a writer--democratic in that the opportunity and the identity are available to all, but tough in that making a living at doing it is a privilege that most societies only support for a few people.
There are two issues here: whether or not philosophy departments are sexist, and whether or not philosophers devalue "subjective" reasoning. You seem to be more concerned about the second issue, so I will address that. It is true that many philosophers (male, female and trans, sexist and non-sexist), especially those of an analytic bent, are devoted to a general and abstract conception of objectivity. Such philosophers are usually willing to acknowledge that experience is particular/subjective, and that different people have different experiences. There is a good deal of room in their positions to acknowledge different social identities.
It is true that some feminist philosophers, such as Sandra Harding, critique general and abstract conceptions of objectivity, claiming that they are supported by an underlying white male middle class partiality. Some non-feminist philosophers (especially in Continental and pragmatic philosophy) also reject general and abstract conceptions of objectivity.
You make an interesting observation about yourself that is important to contextualize. You find a similarity between the kind of economics you are learning and the kind of philosophy you are learning. I dare say that if you were reading Jean Paul Sartre you would find different "parts of your brain" involved! If you are learning the analytic philosophy literature and rational market economics perhaps what they have in common is abstraction and generality? Many prominent philosophers contributed greatly to many fields (biology, physics, psychology), not only to economics. I'm skeptical about any special relation between economics and philosophy.
A mathematician might find his feelings engaged by certain questions. Sir Andrew Wiles was passionate about Fermat's Last Theorem from the age of about ten, I believe. (Say, by contrast, that he took little interest in statistics. Perhaps statistics even disgusts him.) Does any of this "corrupt the purity of the logic" of his (rather long) answer to the question how to prove Fermat's Theorem? No, it just powered his interest in mathematics. Besides, why isn't it possible to be inspired and motivated by a thought or an ideal? The ten-year old Wiles had the thought, 'I will prove the Theorem', and this motivated him and engaged his feelings - and the grown-up Wiles did prove the Theorem. The purity of his logic was perhaps even assisted by his passion.
I used to be very interested in the philosophy of mind. And the fascination was in trying to understand how our ordinary talk about the mind ("folk psychology" as we sometimes say) fits together with what explorations in neurobiology, cognitive science and artificial intelligence tell us.
These days, I spend most of my time thinking about the philosophy of mathematics. And again the fascination is trying to see how technical work in various areas of logic (and set theory, category theory, etc.) interrelates and throws on questions about the nature of the world of mathematics and our knowledge of it. How does it all hang together?
Some of us just like plugging away at pretty narrow areas of enquiry (doing specialist neurobiology, or the technical work in some area of set theory, say): others among us get gripped by the project of standing back a bit and trying to fit things from a number of narrow areas together into bigger pictures. The American philosopher Wilfrid Sellars said that the task ofphilosophy is the latter, to explore “how things in the broadest possible sense ofthe term hang together in the broadest sense of the term.” That remarkis often quoted by philosophers, I guess because it chimes with how alot of us see what we are up to, and what grips us about the enterprise. Certainly, that's how it is with me.
Years ago when I entered the field of philosophy I might have written exactly the same thing as you. Doing philosophy (well) means being willing to challenge those things previously taken for granted. This is exciting (eye opening) as well as, sometimes, troubling. If you are the only person you know who is doing this, it can also be lonely. I suggest that you find some philosophers to talk to.