Hi NW2261,
Is the USB drive you're wanting to transfer data off of an external hard drive? Or a physically larger drive? In some cases, usually for external hard drives a power source is also required to power the drive. The iPhone won't provide enough power to do that.
See more info here, particularly the note at the bottom:
You can use the Files app and other supported apps to access files stored on external devices, such as USB drives and SD cards, connected to your iPhone.
Connect a USB drive or an SD card reader
- Attach the USB drive or SD card reader to the charging port on your iPhone using a compatible connector or adapter.
- You may need the Lightning to USB Camera Adapter, Lightning to USB 3 Camera Adapter, or Lightning to SD Card Camera Reader (all sold separately).
- Note: A USB drive must have only a single data partition, and it must be formatted as FAT, FAT32, exFAT (FAT64), or APFS. To change the formatting of a USB drive, use a Mac or PC.
- Do any of the following:
- Insert an SD memory card into a card reader: Don’t force the card into the slot on the reader; it fits only one way.
- Note: You can import photos and videos from the memory card directly to the Photos app. See Import photos and videos on iPhone.
- View the contents of the drive or memory card: In a supported app (for example, Files), tap Browse at the bottom of the screen, then tap the name of the device below Locations. If you don’t see Locations, tap Browse again at the bottom of the screen.
- Disconnect the drive or card reader: Remove it from the charging port on iPhone.
Note: The Lightning to USB 3 Camera Adapter can be powered with a USB power adapter. This allows you to connect USB devices with higher power requirements, such as external hard drives, to iPhone.
Cheers!