There are issues at different levels for reading Atari disks on a modern PC (or MAC for that matter). We don't have enough information to tell what exactly is the problem with that disk.
In first place there is the low level format. Most USB drives can't read disks formatted with 10 or 11 sectors per track. If your problematic disk happen to have this kind of format, then you need an old school PC floppy (not USB) and a relative old PC with a controller and connector for that type of drive.
The other issue is high level format. Depending on the software and drivers you are using, some disks can't be read at the file level on a PC. This is a software issue. There are ways to read and at least to produce an image on a PC. I'm not familiar with MAC but I guess it can be done on the MAC as well (somebody probably will tell us).
In both cases you can, of course, read the disk with an ST. Then there are several options to transfer the content to a PC. That's doable and usually not too complicated. You can buy an ST, or you may ship the disk to somebody else. You might want to tell us your location on the world and somebody might be able to help you locally.
Lastly, it is possible that the disk is simply damaged and can't be read, not even on an ST. Sometimes the data can be recovered by cleaning the disk. Sometimes not all the disk, but part of it.