I have often read people on Physics.SE (and on many other sites) say that the role of physics is only to provide a good description of nature. For example, we don't ask questions like 'why does x happen?' But is all of science just for providing explanations which match observations? One could say that spirits provide a good approximation of some certain psychological phenomena like split personality (or something else) and misuse this rule of approximating. So, why do we assume that it is the role of philosophy to ask why questions? Isn't it necessary for science to ask the why questions?
That's a good question. Both science and philosophy are complicated and while some may argue this, I would say they have roughly the same goals. The goal of science is to understand the observable world. The goal of philosophy is to understand the world (observable or not). Both of these larger categories have sub-goals that are fulfilled through different sub-disciplines such as chemistry, physics neurology for science and logic, metaphysics and philosophy of science in philosophy.
You have a lot of questions. I hope I can answer the main ones. I would argue that because of these definitions, science is actually a branch within philosophy. Even outside of that, philosophers do ask questions like "why does x happen?" For instance, aristotle's causes (http://www.usefulcharts.com/philosophy/aristotle-four-causes.html) categorize ways to answer that question. Philosophy was around a long time before science. Aristotle was one of science's founding fathers.
The goal of science has changed and become more narrow through time. As some of the previous answers have mentioned, Bacon is a hugely important guy to look towards for answers about what the goal of science is. THe Novum Organum is dry and long and a little feisty, but definately worth reading if you're serious about this pursuit. (http://en.wikipedia.org/wiki/Novum_Organum).
You mentioned spirits as possible causes and it made me think of Comte and his conception of how theories and social thinking develops over time. He wasn't much of a scientist but I think it would be important for you to read about his ideas too (http://highered.mcgraw-hill.com/sites/0072824301/student_view0/chapter3/chapter_summary.html).
Basically, things have changed over time. But everybody is and should be asking why. They just have differentiated over time how they will get those answers. Either through observation, experimentation, mathematics, logic, or whatever.
Also just for fun I'm going to throw this in too. There's a new area of philosophy forming where philosophers are getting up out of their arm chairs and are performing experiments to get answers. (http://en.wikipedia.org/wiki/Experimental_philosophy).
Hope this all helps.
Because science today is restricted to efficient and material causality. This was explicitly recommended by Francis Bacon to focus science on improving the livelihood of man.
However, you are right, it is not a necessary restriction. It is quite possible to discuss formal and final causality (teleology) within an empirical, measurable context. But up to this point there has not been significant work rigorously defining what an empirical science of the latter two kinds of causes would look like.
We should first say something about what is meant by science (at least, science as it is understood today). Science involves:
That is the process by which science takes place. Therefore, it can only answer questions that can be resolved in that manner.
If you subscribe to a materialist view, the story is already over - everything is fully described by matter, there is nothing beyond it, and there is no "why." If you believe there is something to existence beyond what's in nature (the "supernatural"), then there are necessarily things that science cannot answer, because:
So, for example, asking why God made such-and-such a decision isn't a matter of science, because there is no way to reproduce making that decision, there is no counter-factual or control group, and the predictions that have been made from positing a model for such a decision are evidently not so clear as to be beyond all doubt.
Why bodies fall on earth ?
Because, according to Newton's law of universal gravitation :
We study it at school and we still use it in calculations.
This is a clear and meaningful explanation of "why" bodies fall.
If there is a need for other - "more deep" (according to some philosophical traditions) - sense of "why", e.g. final causes (see Teleology), this is a debated issue in philosophy at least since ancient Greece.
Your premise is flawed.
Science does try to answer why things happen all the time. Providing a good description of nature doesn't contradict this.