I'm not an expert, but there are possibly several reasons. I'm not sure which version of iTunes you have, but I do know that songs will not transfer unless either you have the preferences checked to transfer all songs automatically, or you have set specific ones to transfer by selecting them one at a time.
I believe that "transfer all" is unchecked by default, and that means you have to tell iTunes which ones you want on the iPhone. Most folks have way too many songs in there total list to keep them all on a phone or iPod.
To specify which to transfer, the iPhone has to be plugged into the computer, and you have to go to the iPhone settings in iTunes.