Trouble installing macOS - permission denied

Thanks again for your help, Eric. I actually didn’t do the bootable USB, I first tried connecting my laptop to the internet via a cord to the modem rather than wireless and that made it work better. I’m still not sure how it worked in the end, because the erase disk option just showed up again and then I was able to start over and it just worked. But just wanted to say I appreciated your help! I have a “new“ MacBook Air for my younger son, very happy!

Ok, why are all the options in Disk Utility grayed out? It doesn't look like I can reformat.

The two options Apple SSD SD0128SF Media lets me First Aid or Partition, and the OS X Base System under that only has First Aid available.

Thanks for your quick responses!

Thank you. I did that and it went through the spinning globe, then the apple restarted and took me right back to the disk utilities screen that is just the same as before. I tried quitting Disk Utilities and it asks me to choose a startup disk. The only option there is OS X Base System macOS, 10.12.6. I select it and restart and it takes me back to the Disk Utilities. What do I do from there? I tried Reinstall macOS again from there and it has the same Permission denied message.

I have run First Aid a few times, simply because there wasn't anything else to do, but there haven't been any errors. It takes a couple seconds and then its done. Operation successful. Nothing in the details.

My son thinks I need to download the OS onto a flash drive and use that to install from. Is that possible? When I go to the download link for macOS Sierra, this iMac I'm on thinks I want to use it on this computer and says "A newer version of macOS is already installed on this computer. Are you sure you want to download macOS 10.12.6?" So it doesn't seem like there is a way to just put an installer on flash drive. Obviously the days of putting in a CD with the OS software on it are gone...so what are some other options?

Sorry to be taking up so much of your time.