There are many possible reasons. First, the device cannot be another computer, smartphone, tablet, etc.
The device must be in Pairing mode, and the iPhone must be in Settings/Bluetooth; the device should then appear at the bottom of the screen where you must tap it, and follow any authentication that the device requires.
If the device has been previously paired you may need to restore its firmware to factory settings; most devices have a limit to the number of “masters” that it can be paired with.
You can try resetting network settings:
- Open Settings
- Tap General
- Tap Transfer or Reset Phone
- Tap Reset
- Tap Reset Network Settings
- This will erase all Wi-Fi passwords, but will not result in any other data loss.
Perhaps a long shot:
Do you have a 3rd party VPN installed, even if you are not using it? If so, delete the VPN profile in Settings/General/VPN & Device Management/VPN. Don't just turn it off; delete the profile. If that fixes it, you can try reinstalling VPN. However, VPN actually reduces your privacy, it does not enhance it.