It's supposed that the font-family holds several font names for those times that the browser doesn't support the first one. it check the second font name and so on.
I have a desire font and I put it as a first font in the list, but my mozilla browser picks up another font and doesn't recognise my desire font .However when I clear the rest of the fonts. The browser recognise my desire font and apply it in my site .
(I have test this situation in firebug by just temporary changing the style )
How can I find where does this problem come from?
From the MDN page on font-family,
When a font is only available in some styles, variants, or sizes, those properties may also influence which font family is chosen.
For a more detailed understanding of how font-family selection works, please read W3C's rules of font style matchin.
Your first font is only available in a few particular variations and which is why it's ignored when other more complete fonts are present. In absence of other options, FF has to use whatever is available.