many issues can cause what you're getting and what charlie says is true.
i suggest you check into your form and release, too. especially if you're 'new' to shooting a recurve.
often times the arrow will do just exacly what YOU do with the bow...pluck the string and the arrow will fishtail...jerk your bow arm up/down upon release and the arrow can porpoise...grab your bow on release the arrow can fishtail...etc, etc...
keep in mind, the bow is the platform the arrow is launched from, the arrow goes where the platform aims it.
there's plenty of articles in magazines and here about fletching and it's application.
it can be perplexing, but nevertheless, fun in correcting problems.
hang in there.