What is unique to the study of philosophy that specifically taught you to think ?
Such a simple and hard question!
Philosophy originated in the Greek world, about 2500 years ago, with Tales of Miletus (Turkish coast city) and the people around him. (I'm talking from the perspective of Western philosophy here, since that is the tradition I belong to.) It was a radical change in thinking, moving away from mythical, religious and magical thinking. Older texts trying to explain the working of things usually included gods as causes and incantations as solutions. There were some predecessors, such as the Egyptian high priest and architect Imhotep, but in Miletus it started to become a structured and organized approach. The world was no longer explained as being the body or the creation of the gods, and earth quakes were no longer explained as the wrath of those gods. In stead, they introduced a material cause, e.g. water (because it was important for our life as such, and also because it was known as a solid, a liquid and a gas, and therefor a good candidate for being the substance out of which everything else is made), to explain the world. They imagined the earth as being a piece of ice floating on an ocean, and earth quakes as merely being caused by turbulence in the water. They also considered other possibilities to be the "first substance", or combinations thereof (water+fire+earth+art(+ether)), and Anaximander suggested a more abstract first principle (the "boundless").
Those early philosophers were also mathematicians (e.g. theorems of Thales and later Pythagoras), cartographers (Miletus was located at a crossroads between cultures, Anaximander created a map of the world and cosmology) and scientists. Philosophy and science as systems of knowledge came into existence together, they were originally indistinguishable.
The study of philosophy is the study of ideas and of ways of thinking as those have evolved since then. It classically includes sub-disciplines such as metaphysics (the study of the first causes), axiology (the study of values), logic (the study of reasoning), aesthetics (the study of beauty), epistemology (the study of knowledge), ethics (the study of what to do as an individual) and political philosophy (the study of what to do as a group). Many of the sciences have split off from philosophy, for example physics and biology from natural philosophy or psychology from the philosophy of mind - usually by shredding what is being considered as being metaphysical baggage (and thus creating a new implicit metaphysics along the way, which is why even then the study of metaphysics remains relevant). Philosophy is in constant flux: parts split off, parts become obsolete and new issues (discoveries, societal changes, fashions, problems) lead to new parts. That is why I believe that philosophy remains relevant.
Now in my personal case: if there existed something like a major in logic, I would have studied that. However, logicians are now divided over the departments of mathematics, computer science, linguistics, law (e.g. deontic logics, and also the theory of argumentation) and I know logicians in physics, music and other departments. I have considered studying mathematics, computer science and physics (and I intend to enroll on those when retired), but eventually opted for philosophy because I consider it to be at the same time the most profound and the broadest approach. The possibility as a philosophy student to choose a lot of mathematics and physics classes, in combination with all the other subjects, was ideal to create my own curriculum of what I found interesting. The people I work with for my research are mostly mathematicians, because mathematics goes deeper into logic in other aspects than philosophy. In philosophy we learn the modes of thinking from Aristotle over the Christian medieval and Arab (influenced by both the Greek and the Indians) thinkers, to modern symbolic logic (not just classical proposition or predicate logic, but also modal logics, paraconsistent logics, many-valued logics, etc...). Not just how it works, but also ethical and epistemological aspects, and effectively any other aspect deemed relevant, and their implications.