Basically, the elytra's transparency has some odd issues.

From the back, you can see both the front & back transparent textures, but from the front you can only see that side (the back side of the texture is completely canceled out by the front). This even cancels out non-transparent parts of that texture. The elytra texture is basically a box, so I'd assume the transparency would be consistent, but it seems to only work correctly in one direction.
Also, the fact that the right wing is just a copied & mirrored left wing seems to cause some weird issues as well.

I tried my best to explain these issues in the pictures, but I wouldn't consider myself an English master so, sorry if some of the things I wrote in those pictures don't make sense.

EDIT: It seems that the left wing's transparency cancels out most entities behind it, transparent or not (with some exceptions). The right wing seems to cancel out all entities.
And it seems that when held, the ice block renders weirdly behind the elytra when in 3rd person, but not other transparent blocks.