"fishtailing" arrows???

Danny and Frozen nailed it. You are over spined on your arrows. That's why it got better when you put a heavier point on. Also the vanes have got to go! If you look it up, there's a way to check spine by shooting at a target 10' away. If the arrows kick one way they are too heavily spined, and if they kick the other they are too light. Look it up though, I forget which way is which, haha.
Have fun with that recurve! I'm getting back into trad this year as well. Hoping to get one with the longbow.

Have you paper tested yet from a few feet away. See how it's punching paper and if you've got a consistent poor Nock position if you do a lot of bad things can happen ! Easier to fix when you know specifically the problem arrows spin so I doubt the fish tailing is just side to side and more likely a poor paper tune with a knock position coming off center.

are all arrows fishtailin.paper tune it, is it going to left or right , rest might need to be moved, if not that then it might be the shooter

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Originally Posted by Zr2Paul

I. Cut down to 28" with 100gr field tip. I shot them for the first time yesterday and the arrows were "fishtailing" as soon as I release.

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I case you're getting a little confused Paul...some of the advice that is being giving here applies to 'tuning' your arrow with a broadhead....that will be a whole different set of worries once you get your field points to fly straight :)