Android no longer supports "Mass Storage" mode over USB, but rather use MTP instead.
MTP is a fairly universal media transfer protocol used by many devices (i.e. digital cameras), but your car stereo most likely only recognizes USB devices in mass storage mode, similar to what a standard USB flash drive uses. (For what it's worth, I'm not sure if iPhones support mass storage mode either, but it's highly likely that many car stereos have builtin support for iPhone's proprietary protocols so it doesn't matter).
There are actually a lot of good reasons why Android no longer supports mass storage mode, which I don't think I feel like getting into here. A lot of folks complained when Google dropped support for mass storage mode and switched to MTP when ICS was released, but frankly if you actually look into the issue, it's fairly easy to see why supporting mass storage mode is more of a logistical nightmare with today's high capacity devices. (A big part of it is that in order to present a drive or partition to another device in mass storage mode, it has be unmounted from the device itself, which obviously creates a ton of problems if your phone can no longer access the internal storage partition while it's hooked up to your car/computer/whatever).
Long story short? You're most likely not going to find a "solution" to this specific problem.
Hopefully, now that MTP has been standard on all Android devices, more car stereo (and other product) manufacturers will start to provide support for it. Until then, you're probably stuck using AUX or BT. For me, BT works awesome, but if your head unit doesn't support that either, I can see why it would be frustrating.
EDIT: Here's a reddit post on this issue that describes a lot of the reasons why mass storage mode is no longer supported...
http://www.reddit.com/r/Android/comments/1aqjd0/why_do_new_versions_of_android_not_support_usb/