Why is the word "n.i.g,g,e.r." offensive to some people?:
What an obtuse question!

Simply because that word was used by certain people precisely <as> a term of offense to describe 'some other people'.

Your question would have much more validity if it were "why did white people decide to use that word as a term of offense in the first place?"

Yes we know that black people use the word within their own community, just as gay people use the word 'queer'. But that doesn't change the fact that the word was first given currency as a deliberate insult.