OK, classic car people are not nuts, they have certain reasons for driving classics. I am a classic car guy myself and after some introspection I can tell you what the motivation to drive them is: Design: classic cars possess a certain character not to be found in contemporary cars, since old cars were designed more freely, i.e. not constrained by regulations (safety, interior/exterior/engine/...) Most classics have features which unmistakingly belong to this or that car. You drive a car which stands out in the grey mass of traffic.
Classic cars have better looking engines (yes, the looks of an engine is also important). Nowadays engines abound with electronics and are ensconced underneath plastic covers.
Classic cars are often straightforward to maintain (I am not talking about Ferrari V12's or Pegaso!). You can do a lot of maintenance yourself. Parts of an old Ford say, are cheaper than their modern day counterparts.
Driving a classic without ABS, traction control etc. is more challenging, and a lot more fun too (how I love performing a humble powerslide with my old banger once in a while).
Old sports cars in particular are most rewarding to drive, they wonderfully convey the thrill of driving (a quality I often miss in modern cars). They require some physical strength from the driver, they get hot, they are loud and there is no power steering. The aircraft feeling cannot be denied.
Many old sports cars are revolutionary when it comes to design, they therefore belong to automotive history and can still thrash modern cars. E.g. 1954 Elva 1100cc 0-60mph in 9.5sec. An excellent performance for rudimentary engines, which in saloon cars would need five years to achieve that speed. So far for an Elva, and I haven't started to mention the Lotus and Coopers yet!
It is a shame though -and this is my personal opinion- that old racing cars have benefitted from tuning that wasn't available yet back in the old days. Now, they can squeeze even more power out of those engines, in that they are verging on modern car figures. Old cars should keep the modifications from before. if those cars hadn't received modern treatment, one would be even more impressed with old school tuning. Engineers were also capable of wizardry back then. But, as is always the case in racing: he who has most bobs wins. I have heard engine prices which are truly astronomical, whereas in the 50s or 60s they would have cost a fraction of their current value. If old cars keep coming closer to modern ones, what is the point in having a classic?
In addition, sports car driving (and racing in general) was a true feast for the car enthusiast. It's a pity I wans't born yet to experience it. I know older people who say classic cars are totally outdated and retarded; some of those people despise old cars, others race them. The latter are hypocrits who modify their vehicles to modern standards. What a way to share what once was the height of car design with young people. Car should be driven like they used to: period mods and original livery, and most desirable genuine drivers at heart.
Classic car people are not nuts, some are just not righteous.