How come my iPod Shuffle does not connect to my radio?

Don't understand the question... In what way are you expecting an iPod shuffle to connect to a radio?

You should refer to the user docs for your car radio or home stereo, to see a list of supported devices. iPod shuffle may not be supported for this purpose, since it connects to USB through the headphones jack (not a dedicated docking connector like other Apple devices).

If the radio has a auxiliary audio input (usually looks like a headphones jack or maybe "RCA" connectors), you can play the shuffle through the radio's speakers using the appropriate audio cable.

Alternately, buy a cheap USB flash drive for this purpose. Here's one that barely sticks out of the radio's USB port for less than $10, with 16x the storage capacity of an iPod shuffle

https://www.amazon.com/gp/product/B00812F7O8

As I mentioned, the iPod shuffle uses its headphones jack for the dual purpose of audio output and data connection (to a computer). All other Apple devices have a dedicated multi-purpose docking connector for data connections. This may be the design limitation that makes it not work with your radio's USB port.

I recall that my old 1st gen (white plastic) shuffle worked with a car radio's USB port. But the 1st gen shuffle is the only shuffle model that has a built-in USB plug (for docking) and a separate headphones jack. All later shuffles use the headphones jack for docking.

(duplicate post)