It has everything to do with latency. Most software takes more than one frame to react to input, so halving frame time noticeably reduces latency. I'm also an "old school quake head", and I'm just as sensitive to latency. I stuck with a CRT until true 120Hz LCDs became available, because they are the first LCDs that aren't an obvious step down from CRTs. Even so, in a side by side comparison the CRT has slightly better motion quality, so we really do need 240Hz LCDs.
Note also that CRT flicker is a good thing if you're displaying fixed framerate 60Hz content (and there's a lot of that out there), because it's the only way to avoid sample-and-hold blur without adding more latency and motion artifacts with interpolation.