It's about mechanical empathy and greater control. Mechanical empathy is where you just really know a machine with character, and know how to handle its foibles, and it's like an extension of you. Where earlier automatic transmissions were less efficient, there was greater efficiency to be had from a manual transmission, but since dual-clutch automatics, that's less true. Even So, an automatic transmission can't know what you're thinking (yet), and so can't down/upshift when you want it to.
It's like running Linux. At some point it's just another OS, so what difference does it make? And for some, it doesn't make a difference. For others, having more control, and being able to dig into the guts of a desktop Linux system and replace whatever you want let's them feel more connected to the computer, making it less of a mysterious box that operates on magic and black smoke, and more of a predictable machine.