Catweasel mkIII and mkIV here, a bit expensive, but great to use.
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Right, so, definitive answer time:

Why in the name of all that is sacred can't I read an Amiga floppy disk in a drive that is connected to my PC motherboard?? I can create a PC-readable floppy in my Amiga using the exact same drive - it just makes no sense is all.
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Because the Amiga uses a customer disk drive controller that changes how the drive is used to read and write the tracks and sectors onto the disk. A PC floppy drive controller is not capable of reading or writing how Amiga disks are formatted.
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So where is the controller? I bought a generic PC floppy drive years ago and used it okay with the Amiga, so I'm guessing it must be on the computer's motherboard and not on the board inside the floppy drive. Does this mean that, theoretically, I would be able to reprogram the controller chip on the PC mobo to be able to read/write to Amiga disks? Is it possible to override the controller through software?
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The controller is on the Mobo of the Amiga the controller on the PC cannot be reprogrammed to accept Amiga disks in the same way as putting a PC High Density floppy into a Amiga doesn't mean that you can use HD Floppies. It's far easier to use transADF and transADFGUI on the Amiga to create ADF's and then transfer onto Floppy. Either that or get hold of a Catweasel III.
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And to explain the Catweasel controller. It is in effect an Amiga floppy drive controller on a PCI card, therefore giving a PC the ability to read and write Amiga disks using a standard PC floppy drive.

However the Catweasel controller does go much further than this because it also has the ability to read and write any other formats such as C64 5.25" disks, Atari ST and many more. Plus later versions also allowed the addition of a C64 SID chip so you could listen to SID tunes exactly as they were meant to sound, instead of through PC emulation.
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