Pen drive is causing my MacBook Air to freeze up

Drickbay wrote:

What does “Volume Could Not Be Unmounted” mean? That’s a bit worrisome..

You ran Disk First Aid on the current startup disk. Normally Disk Utility likes to completely dismount the volume being scanned and/or repaired, so that no other application or part of macOS will touch it. In this case, that was not possible. You asked Disk Utility to fix the current startup drive – the one that was in use, and could not be taken out of use. A bit like asking a mechanic to repair a car engine while the engine was still running.

Thus the messages that the computer might stop responding, that the volume could not be unmounted, and that Disk First Aid was using "live mode." In that mode, Disk Utility's ability to repair any errors that it did find might be limited. Ideally you would start up from an external startup disk if you wanted to scan and repair the internal one.

You can boot into recovery mode where you can run First Aid on the internal boot drive.

If your Mac starts up to Options with a gear icon - Apple Support

Edit: I assumed you are using an M-series Mac......here is a better link for accessing recovery mode (good for both Intel & M-series Macs):

How to start up from macOS Recovery - Apple Support

FYI, you should always post the exact model of your Mac (or device) along with the version of macOS being used. You can get this information by clicking the Apple menu & selecting "About this Mac".

Even if you closed every application, the operating system itself was still running off that drive, and still using it.

A startup disk is one on which a valid copy of macOS is installed. Making bootable clone backups of your main drive used to be a very useful tool for backup and system recovery.

Carbon Cooy Cloner and SuperDuper! are/were the two third-party applications that you could use to make such backups. Normally you would make them to an external mechanical hard drive or external SSD. “Pen drives” can be used, if large enough, but aren’t the best choice in terms of long-term reliability and opportunities to misplace them.