Here's what rhymes with counterintuitive.

Consider these alternatives

mystifying / dying unsurprising / rising implausible / plausible wrongheaded / longheaded illogical / logical retrospect / effect anachronistic / characteristic quixotic / logic trite / right unwise / size unsatisfying / dying counterproductive / productive unsurprisingly / surprisingly juxtaposition / position cliched / made instructive / destructive uninitiated / dated simplistic / characteristic unappealing / feeling apropos / no