[Taken and expanded upon an answer I gave over at r/AskPhilosophy]
The common understanding of philosophy is that it is a "subject" among other "subjects" - standing alongside art, physics, history, mechanical engineering, biology, and so on. Where all of these subjects study their corner of the world, philosophy itself is supposed to have a corner of the world which it studies - a range of specialist questions tentatively related to other fields (as certain parts of physics relate to certain parts of engineering) but otherwise in a sphere of their own. And yet the one thing we immediately notice is that philosophy seems to show up everywhere. There's a philosophy of art, of science, of psychology, of history, etc. - what accounts for the ubiquitousness of philosophy in all of our other subjects?
You might say the "philosophy of history" is only an area in the subject of history, along with other areas like medieval history, the history of medicine, Chinese history and so on. As we could get on with the business of history without studying Chinese history (though we'd perhaps be poorer for it) so we can get on with the business of history without studying the philosophy of history. But is this the correct way of coming to terms with the ubiquitousness of philosophy? How are we going to figure this out? Well, it seems to me like the most sensible way would be to see if philosophy permeates the rest of the subject, so that a "philosophy of" is not merely a possible and non-essential theme which we can study within a subject, but is rather an essential directive lying at the heart of the questioning which a given subject takes as its own.
First, a little history. Before the first academy was founded by Plato, there were no explicitly divided subjects. Thinking was free to roam, and this thinking was known as "philosophy". Just as a discussion we would have with friends can wander unimpeded along "subject lines", from ethics to politics to philosophy, so it was with the first thinkers. However, when the Academy came into being this freedom of thinking was split into three "subjects": physis, ethos, and logos. From there the phenomena uncovered by thinking, previously discovered as a whole by thinkers, were formally divided into regions. Where the first philosophy had simply thought the world in an holistic manner, now thinking had become specialised.
And indeed, we're still a part of the wave of "splitting" and "isolating" which our Western way of being fosters, and which led to Plato's tripartite scheme. So what does this have to do with justifying philosophy? Well, we have now gained an insight into the notion that philosophy as a thinking unfettered to any region of phenomena, initially, covered all phenomena now split into regions of beings along "subject lines" (which are now manifold). Thinking has thereby found itself bound to different regions of beings. Perhaps it is this common origin which accounts for the fragment of philosophy we find everywhere, a shard of that shattered first questioning which still remains in every subject now isolated from its ground in original thinking.
And what is this shard? Well, when a subject conducts its investigations it makes a variety of tacit presuppositions. Law, for example, presupposes a notion of responsibility (tied to an understanding of free will and therefore an understanding of the being of man), along with notions of good conduct, justice, etc. Where law pushes ahead on the basis of these notions, the "philosophy of law" looks backwards to clarify these fundamental concepts and assess them for soundness. But it is philosophy proper and not just "philosophy of law" which deals with these questions! These questions did not first emerge with the formally defined subject of law but have demanded attention throughout human history. How to live good lives is a question which emerges not out of a detached thinking about things, but is rather demanded of us by simple virtue of the fact that we first find ourselves having to live in some way. We did not and could not choose this way of being in which we have to choose (the way of being which makes possible moral and therefore legal responsibility) - the question of how to live blossoms like a flower from the soil of our very being.
Now, the philosophy of law is the manifestness of law's rootedness in this original questioning which, before something like law is possible, must already be supposed. We need not explicitly presuppose these notions (indeed, as we have seen their presupposition emerges from a question posed implicitly from out of the simple fact of our existence). That we don't need to make these presuppositions the object of an explicit enquiry and can "get by without asking them" is the ground of the reason why people typically see philosophy as a non-essential subject among other subjects. However, philosophy has already taken place in the very fact of existence which summons the investigations of a subject forward. And if we are at all concerned about the nature of the investigations of these subjects, founded on implicit philosophical assumptions, we will study them and assess them. How would the legal system look, for instance, if everybody accepted that there was no free will and therefore no responsibility? How do the findings of quantum mechanics look dependent on your stand in the realism/anti-realism debate? Indeed, even the conceptualisation of neural mechanisms bear the mark of implicit philosophical assumptions. Calling the neural system dealing with detached contemplation "the default mode network" only makes sense if you begin from cognitivist assumptions about the being of man.
So any question of justifying philosophy has already come too late! Philosophy as first thinking is presupposed by all subjects - to ask for justification is to commit a category error. Philosophy is not like a subject among other subjects. Philosophy is the explicit ontological investigation of fundamental concepts necessary for the pursuit of any and all ontic investigations. As these presuppositions arise from everybody's existence, in some sense everybody is a philosopher - which is why we can all ask these questions, and how we can step into various specialist subjects on the basis of our pre-conceptual philosophical understanding.