Do you have any tips on how I can fix that? I'm not trying to do that. Maybe forcing my arms to stay at my sides?
First off, props for taking constructive criticism.
When it comes to looking less stiff overall, I find that actually relaxing and not over-thinking as you ride helps more than anything. Just "feel" it, and your riding will look more natural.
You are also stiff on your rail moves. If you stiffen up during jib tricks, you will not only look super awkward, but you're also more likely to fall. When you hit a box or rail the right way, you let your momentum work with you, and after a bit of experience, your muscle memory will take over and you'll look better as a result.
As for your spins in particular, try to wind your body up more before the actual spin. Then, just before you actually start spinning, make sure your body is "open" to the spin and turn your shoulders into the direction of the spin.
It's hard to explain it without visuals. Check out this climp from "Jumping with Jussi" for an idea of the exact mechanics of how to spin: