Recently I was engaged in a reasonably impassioned debate about why anyone should wish to philosophise. The question had never really occurred to me before since I’m not entirely sure it’s possible to live life without doing it. To me philosophy is a natural consequence of the ability to think and our existence as part of society.
What is Philosophy?
This is a question I can’t hope to answer definitively, in fact the distrust in which philosophy is held in many parts may be rooted in the difficulties of answering this question. However, I shall give use the term as defined as:
The systematic inquiry of the fundamental questions concerning, among other things, the nature of reality (metaphysics), the justification of belief (epistemology), and the conduct of life (ethics). 
This definition has the consequence that even the dismissal of philosophy as a nonsense has to be considered a philosophical view and is thus self defeating since the only way to justify it would be to use philosophical arguments to do so and an unjustified argument has little basis on which to be considered persuassive.
How is Philosophy Actually Helpful?
Well, for one thing it’s the fundamental base of our political and legal systems. There can be no normative political theory which is not based in ethical theory and theories of human nature. These subjects certainly overlap with the sciences - biology and psychology in particular - however, this doesn’t negate philosophy as a subject, it just assures its position within the realm of human thought.
Similarly, philosophical thought can bridge the divide between science and reality and, through logic, underpin all of our mathematical and scientific progress.
Why Should Philosophy Replace Intuition?
Short answer: it shouldn’t. However we have to understand both that intuition has limits to its applicability and that intuit