Why I can't restore the phone with iTunes

You have 3 points of failure here and can methodically go through them to figure out what the issue is.

1. Cable - By far the sneakiest yet easiest problem to fix is a faulty cable. It might show enough info for you to think it’s working however it may not be, and the only way to know would be to try a different cable. If you’ve tried a couple different cables(preferably an official apple cable that came with your device) and nothing is changing, then you can move on to the next point.

2. Restore/DFU - You need to make sure that you’re trying to reset your device using DFU mode, not trying to restore the device using the prompt on screen. To do this properly, you’ll need to hold down both the Home button and Lock button for 8 seconds. Then release the Lock button and continue to hold the Home button(If the Apple logo appears, the Lock button was held for too long). Nothing should show up on the screen at all, meaning you are in DFU mode. If the device shows a prompt telling you to connect to iTunes, you’ll need to try again to get into DFU mode. Once in DFU mode, follow the prompts on iTunes or Finder to reset the phone. If you’re confident that you’ve reset the phone in DFU mode and it is still not working, then you can move onto the next point.

3. The Device - Assuming your computer is all up to date and wasn’t the problem, then the only thing left is your device. There may be an issue with the lighting port that is limiting the reset process through cabled connections or a seperate issue with the logic board entirely. If you’re unable to test the lightning port yourself, maybe take it into a repair specialist that can assess it for you, along with the logic board.