It would be very helpful if those who state "Honda automatic transmissions are picky about the fluid used" and "use Honda ATF only" would provide some evidence for such statements.
It is quite interesting to read through applicable threads in the Odyclub forum (Honda Odyssey vans) and note the change over the years as posts shift from "use Honda ATF only" to "Maxlife and Amsoil (and others) have shown good results." I won't pretend to have "the" answer, but with a sample size of two (Odyssey and Pilot), Maxlife, Castrol ATF for Imports, plain Dexron III, and Dexron VI have given acceptable service in terms of the driving experience. Of course, who knows what might happen after 200,000 miles, though reaching that point with the transmission in a 2001 Odyssey pretty much falls into the category of miracle. While waiting for that milestone to arrive, I'll keep using Maxlife because it gives shifts that are both quick and smooth, because as a synthetic it might breakdown more slowly than other ATFs, and it has given good results for many Odyssey and Pilot drivers.