I am not a particularly educated or intelligent individual. If this question is easily answered, forgive me. As I can think of no answer, I am compelled to ask. I'm afraid this line of questioning ends up in circles but I don't think it is a nonsense question. We have (some debate this) conciousness and independent will. Why? It seems unnecessary as a survival mechanism based apon David Chalmer's assessment of "The Hard Problem of Consciousness". Of'course the immediate question can proceed further based on that to, why do we even care to survive? There is obviously a lot more to that whole line of questioning. I'm trying to cut through quickly dismissed answers. If this sounds like the child's constant why why why? It is. What I don't understand is why the question isn't, "how?".
How is applicable to the precise situation that occurred. Why is applicable to a whole host of hypothetical what-if worlds which, if understood, may make life easier if one of those hypothetical situations arise again.
How a person died in a car accident is one thing. Why they died is a question which may spawn changes in seatbelt design to save other lives. Both are indeed important, but they are important in different ways and to different people at different times.
In your question, you seem to suggest that a sense of "its just what living things do" is not really a comforting answer. However, that suggests that your question starts to rapidly jump from "why do we ask why" to questions regarding the ultimate meaning of life. That is a topic which has received a great deal of philosophical study, although I do not believe a meaningful consensus has been reached on the topic.
As you know humans have (more or less) a quality/habit of seeking truth. And those who have higher intelligence seek higher levels of truth. Seeking truth is one of the main characteristics of humans. For this he needs new pieces of information and so he uses Wh-questions frequently. To find out the truth about phenomena, happenings etc 'Why-questions' are necessary.
Those who have higher intelligence would not satisfy with a unscientific/simple answers. Comparatively 'Why-questions' are the difficult ones because, for getting answer to them he is often compelled to put several steps back to discover the truth which is rather difficult. (I mean,) Often, to other Wh-questions he gets answers with less effort; but 'Why-questions' are not so. Actually he asks other Wh-questions also frequently. But it is because of their easiness they seem latent or unnoticed .
It is interesting to looking at trying to get AIs to learn. Wu & Tegmark's 'AI physicist' is the best example I know. It seems like we can relate 'how' questions to rote learning, to implications of an event or statement, in relation to our body of experience, or integrated knowledge. But 'why' questions do something else, something computers struggle with. I feel the best model is that of 'strange loops', developed by Douglas Hofstadter.
The mathematician Godel proved with his Incompleteness Theorem, that within any reasonably complex system of symbols based on rules or axioms, true statements can be made which aren't provable from those axioms. From mathematics, and computing, that has been our model of human thinking, that it is all kind of 'how?' questions, and everything would just follow logically when we understand the Grand Unified Theory, the answer to all 'why?'s. Incompleteness shows there must be more to how we work. There is a funny broader statement of this taken from the same source as 'pulling yourself up by your bootstraps', which gave us the tech phrase bootstrapping: Munchausen's Trilemma. It says, any chain of explanation reduces to circular logic, infinite, regress, or 'because I said' so - parents of small children will be well familiar with these fall-back positions as every answer gets another 'why?'. The Adventure's Of Baron Munchausen that this references piles paradox on paradox, in funny ways.
I see 'strange loops' as a way to answer the trilemma, and understand how human minds do what they do, without denying the usefulness of logic axioms and so on - to not throw the baby out with the bathwater. What Hofstadter noticed is that 'why?' questions can 'pop us out' of layers of explanation. We set up hierarchies of explanation, a classic example is: atoms, chemistry, biology, sociology, cosmology. And then he noticed we are happy to do what computers and mathematics doesn't like, we like to loop back round - like say the anthropic principle, the idea physics fine tuning of constants might result in some way from being a given if there are minds, so no mind could look out and ask 'why?' if the constants weren't compatible, weren't 'just so' to allow a complex universe. Here are some more examples of strange loops, because I can't really do the idea justice in a concise way. It's crucial to note strange loops can involve recursion, thinking about ourselves, as units in our thoughts, which can really tangle thought-hierarchies in ways maths and computers with no subjectivity cannot, and that can create strange and wonderful feedback loops..
So, in this view minds are not rule followers, and they are not just trying to make a coherent structure reaching between very small and very large with a place for us inbetween. Instead they are constantly weaving a fabric, which changes threads and weaving style, looping back on itself, sometimes the whole cloth becomes just one new thread in a bigger fabric, and sometimes we unweave a section, sometimes we unweave huge chunk look very closely at the threads, and begin again.
I link this model of minds to Dennett's idea that we exist as 'free floating rationales'. Also to Buddhist ideas that awareness is fundamental, and has a universal quality - it is the weaver, not the threads.
When we ask 'why?' we take a moment away from our weaving, we think what field did these threads come from, what will this cloth be for, how do I fit in to that story. And we realise all those questions, all our knowledge and ideas, are more threads, to be rewoven, or unpicked.
Edit to add: I look at all these answers, and think they are all susceptible to, 'Why though?'. FOXP2 is a gene complex all animals with language, and birds that sing, seem to have. All will babble, from birth. Songbirds raised only around humans, learn human tunes. Humans raised by wolves can never learn human language without hearing it, beyond a certain age. So, at the deepest level, we are monkeys who ask 'why?'. 'Why?' is our song, our answers are our shifting shimmering, plummage.
"Tiger got to hunt, bird got to fly;
Man got to sit and wonder 'why, why, why?'
Tiger got to sleep, bird got to land;
Man got to tell himself he understand."
-Kurt Vonnegut, Cat's Cradle
I think this ultimately boils down to Natural Selection: Simply put, curiosity has proven itself to have survival value. Combine that with ever-increasing intelligence also having survival value, and eventually yielding the capability to create leisure time, and you end up with creatures that regularly ask 'Why?' about a wide range of things most of which aren't directly tied to immediate survival.
'Why' questions are a concomitant of the capacity to make choices. For animals that run primarily on instinct, 'why' questions would be irrelevant. When such an animal sees (say) another animal that it recognizes as a predator or as prey, a set of responses kick in that inform its actions. while many animals are intelligent enough to adjust their behavior mid-stream according to circumstances, the overarching activity is preset. The 'what' and 'how' are givens — hunt or fight or run — so there wouldn't be much point in them asking 'why' they behave that way, even if they had the capacity for it.
Humans aren't bounded by instinct to anything like the same extent. When a human sees (say) a chicken, the human doesn't feel this overwhelming 'prey-food-must-kll-eat' impulse, they way that (say) a cougar might. A human looks at a chicken and thinks: "Well, I could eat this chicken, or I could keep it in a cage and eat its eggs, or I could make a pet of it, or I paint an image of it on my cave wall..." There are lots of different things that humans might do with chickens. Choosing between the various options automatically implies a consideration of different reasons or values; it implies a purely practical question of why this use of a chicken might be better or worse that that use of a chicken.
If you look at a cougar and ask it why it wants to eat a chicken it won't have an answer, because eating things like chickens is just what it does. It has no other use for a chicken than to eat it. That is decidedly not true of humans.
The reason this kind of complex choice process is evolutionarily adaptive is that it allows humans to be generalists rather than specialists. Strong instincts make for great specialists; cougars are apex predators because evolution has hammered out extremely effective hunting instincts in the kind of environment that cougars are accustomed to. The problem with being a specialist, though, is that if the environment changes sufficiently, it's impossible for the creature to adapt. That species goes extinct (they way that tyrannosaurs went extinct) and a new creature with better adapted instincts takes over that creature's role. Humans, however, can shift and change according to circumstances. They are cognitively adaptive instead of biologically adaptive, and that allows them to respond to changes in their environment much more rapidly and effectively than other creatures.
The downside of this fairly practical adaptive mechanism is that it allows us to entertain some fairly 'out-there' options. For instance, one might be dreading an upcoming office meeting and think "Geez, why couldn't I just let some cougar eat me so I don't have to deal with this crap..." There's no shut-off valve for the capacity to make choices, no easy way to fall back on the sweet life of mere instinct. Plenty of people try, of course — sex and drugs and rock and roll; candy is dandy but liquor is quicker — but that is always a deflection of responsibility more than a real retreat to instinct.
It's a mixed bag, I'm afraid. Once we start having choices between various 'whats' and 'hows' we are forced to start asking 'why', but once we start asking 'why' we can't just turn it off when the options become distressing or difficult. We either move forward into it and adapt, or retreat from it and descend into unconscious misery. People can choose to do either, for their own reasons.