Thats most likely the problem. The feathers can give and literally fold out of the way. The vanes cause huge ammounts of contact that will kick the back of the arrow sideways as it leaves the bow.
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Fishtailing can be caused by nocking point being too high or too low as well, takes time for flight to correct if this is the case.
I have also heard of the balance point of the arrow having a lot to do with it. More specifically how far forward of center the balance point is. I think its referred to as FOC "Front of center". Look it up, it may help.
MC
The following link will help on the F.O.C. calculation, have a higher number than they recommend is not a bad thing as far as arrow stability in flight and penetration. I did confuse fishtailing and porpoising, apologize for that. Thanks for clarifying Zr2
http://www.backcountrybowhunting.com/articles/calc/
I think those arrows are too heavily spined they are meant for a heavier bow and the plastic vanes are probably making it a lot worse get them fletched with feathers with a helexical twist and that will help stability.
Attachment 26433Attachment 26434your rest is out of whack. move your rest out alittle at a time until
you can shoot with straight cuts through paper
Get some aluminum arrows with feather vanes.
You are over spined by a fair bit. That and if you're shooting off the shelf plastic vanes won't work either. FOC won't help your arrow flight enough if you're out of whack. The shorter the arrow the worse the problem will be. Ways to make a overspined shaft work is lengthen the arrow or heavier tip. Both make the arrow bend easier thus reducing the spine and allow the arrow to bend and clear the riser