“An error occurred while downloading the selected updated. Please check your internet connection and try again.”
I was trying to update to Big Sur 11.5.1 to patch a zero day vulnerability.
I clicked System Preferences -> Software Update -> Update, it had some Terms & Conditions I needed to accept, and then told me it would take up n Gigabytes of space. I had enough space, so went ahead, and then got the dreaded error message above.
Whilst it looks like an internet connection issue, apparently the error message is totally misleading and is nothing to do with your internet connection at all. There are loads of suggestions on the web around restarting in Recovery Mode and reinstalling macOS, which sounded very… intense.
Then I read somewhere that you can try installing the update via the App Store. Sure enough, I clicked on the App Store, searched for “Big Sur”, then clicked on “Get”, which opened the same “Software Update” window I had already opened, but it triggered a “Searching for updates” animation and then found an update that was multiple times larger than the one I was initially trying to download. I didn’t have enough space, so the update failed.
I deleted a few GBs of files and tried the update again. This time, it worked! 🎉
I’m not sure if going via the App Store worked, or whether in the initial update attempt I didn’t have enough space (and it was perhaps just under-reporting the amount of space it needed). If you’re facing this issue, try making loads of room, and try updating via the App Store. Good luck!