I have seen that most of the film music directors use keyed music instruments for composing music. I hardly saw directors use other instruments like strings or wind instruments for the same. What would be the reason for this behaviour?
A piano/keyboard with its usual 88 notes covers the range of most other instruments put together. A lot of instruments have a range of two or three octaves only. A lot of instruments can (usually) only play one note at a time, whereas keys are capable of many.
So, someone who is writing music for several instruments has it all covered with piano/keyboard. Want to hear roughly what a bass line or piccolo part is like, in its correct register? Use a keyboard. Want to hear what eight different notes, some high, some low, sound like together? use a keyboard.
By the way, a director is usually the one who conducts the other musos, although, chances are, he'll be sitting at a keyboard for the performance. It's a composer who writes the music - usually, as you say, at a piano/keyboard.
Because on a piano you can try out single-note melodies, block chords, broken chords, polyphonic musical lines... and all at once, over a wide range. A composer CAN get along without keyboard skills, but it's hard work. Particularly if he's composing the sort of music that will end up on paper as notation for other musicians to play.
A film composer usually uses as synthesizer/midi controller connected to a computer. Same with any kind of music producers (rap producers, edm producers, pop music). For music production there is no other competition to keyboards. Once you connect it to a computer, you use software known as Digital Audio Workstations (DAW) such as a FL Studio, Ableton, Logic, Protools to create music and any sound you can imagine. So you can recreate an orchestra if you wanted to just from a little laptop.
So you don't need need to physically own alot of instruments (strings, wind instruments) you basically just need a computer and a midi controller connected to it to create any sound/music.
MIDI keyboards have become de facto input method of musical notes into computers. Composers use MIDI keyboards to create musical scores like writers use QWERTY keyboards to create prose.
Moreover, piano is compulsory instrument in most music schools, so anyone who received formal musical education can play piano.
That's not really the case. Not all conductors use keyboards.
Of course, there are a lot who use them, and they do it because they can get the picture of the piece they are dealing with. They can have a better idea of the music they're going to perform as conductors.
If you used a violin, for example, you could not have more than 4 sounds playing simultaneously, with a keyboard you can have at most 10 sounds at the same time, which would represent the sound of 10 instruments. If you had an organ, this could be even better because you could use your 10 fingers plus your 2 feet, that's 12 instrument families at the same time. That is more than enough to represent instrument families in an orchestra.
On the other hand, electronic keyboards are widely used as they enormously facilitate interaction with computer music software.
In my case, as a classical musician, I use keyboards and when carrying one is not possible, I use any harmonic instrument, be it a guitar, a cuatro and when none of those are at hand, I use my recorder.
Another point I haven't seen mentioned here is that composing music, in your context, sounds like getting it scored on paper for others to read. Writing music on paper is a very visual process, and the piano is a very visual instrument; every key is directly related to the note it's playing, and no other note.
On a violin, for example, playing a B on the low string is really playing the A string and shortening it a bit with your finger. But on paper, a concert B isn't related to concert A in that way. Speaking of concert instruments, composing music on something like the Bb Clarinet would be a bit of a struggle (unless you were writing for other Bb instruments), as you would need to transpose every note.
The piano is great because that's the note, right there. You don't even have to be able to play the piano to play the note. You just point at it, poke it some, and the note comes out.