I was thinking about it - the Bat's worked with more magicians than most magicians in the DCU - Zatanna, Jason Blood, at least one Dr Fate, Mantou Raven, Mantou Dawn, Raven, and no doubt others who aren't currently coming to mind immediately...then there's Alan Scott, Aquaman, Captain Marvel, and others who aren't magic users as such, but have magic-derived abilities. Then seeing Superman taken down by magic.
I don't have a problem with classifying magic as 'a science we haven't codified, yet', so long as he acknowledges it exists, and works, but disbelieving it entirely goes beyond scepticism into outright denial.