Nope, that's a male to female. The technical name would be "USB type A plug to USB type A receptacle", and that's the correct cable to use with a flash drive, it's essentially like a USB extension lead. You couldn't have been using a male-male cable because the flash drive physically wouldn't fit in the end of it! Unless the cable itself was broken in some odd way (unlikely) then it wouldn't have caused your flash drive to break at all, this must have been through some other means. Might've taken a knock or something similar, or might just be wear and tear - these things don't last forever.
Was that what you wanted to know?