I think of Zeno's paradoxes as trying to appeal to the essence of dissolved questions. Sort of like, having decomposed "does the tree make a sound?" into "does it produce vibrations" versus "does it cause auditory experiences", somebody comes along and says "but does it make a SOUND???", emphasizing the word "sound" to appeal to your intuitions and make you feel (incorrectly) that something in reality has yet to be resolved. Here, "motion" plays the part of "sound", after a faulty reduction of "motion" into "series of still-frames".

But if I were to be that guy who comes along and says "sound" until you feel uncomfortable again, I would say "What's to say your arrow doesn't just teleport from one frame to the next, rather than 'move'? Can't your 'change from one frame to the next' also be broken down into a series of frames?"

I wouldn't lose any sleep over it, since you're obviously right and anyone who denies motion is obviously wrong, but that's at least where certain hapless philosophers are coming from.