Hi, EMikita. Thanks for reaching out! I'm an Independent Advisor and a Microsoft user like you, and I am here to work with you on this issue.
When you open the Media Creator tool, you have to choose between "Upgrade this Pc now" and "Create installation media (USB flash drive, DVD or ISO) for another PC).
For what you want, you have to choose the second option (Create installation media). Then, after selecting the Language, Edition and Architecture, you'll have two options> "USB flash drive" and "ISO file". Choose the first one and you'll be able to select your USB flash drive.
You you're already doing that, then you probably don't have space in your hard drive for the Media Creator tool to download the ISO file before is moves it to the USB flash drive.
I hope this helps! Please let me know if that works for you, ok?