So the UESP states this:

"Spells can be cast for free with 100 Enchanting skill, all 5 Ranks in the Enchanter perk, and the Insightful Enchanter perk. You enchant helm, chest, ring, and amulet with a 25% spell cost reduction in a specific school for a total of 100% cost reduction. With the Extra Effect perk, an additional magic school can be cast for free."

Well, I have 100 Enchanting. I have 5 ranks in "Enchanter". I have the "Insightful Enchanter" perk. Yet, when I go to the altar, it only shows up as 15% reduction, not 25. So...what's the deal? I'm using a Grand Soul.

Also, it won't let me choose rings OR amulets to enchant the spell reduction. It says "Chose enchantment cannot be applied to this item." Lol?

you must have 5 basic enchanting perk + the first perk in the middle to have-25%. you can enchant necklaces, rings, armors or helmets
what platform r u playing on?

I think certain enchantments only apply to clothes while others can be applied to weapons etc. I ran across the same thing recently. Wouldnt make sense for a ring to do shock damage if you cant hit with it type of thing i guess.

Thanks for the info LordWooFakFak64

...as stated in the OP, I DO have those perks. And every single source on the internet says you can enchant rings and necklaces with the skill enchantments, yet my game won't let me. And I'm on the 360.

http://www.youtube.com/watch?v=eyyhNk9gICQ

Watch this video, he clearly has the skill enchants on his rings and necklace, yet I can't do that in my game. Also, I just went to radiant rainment, she had a ring of peerless alteration that reduced mana cost by 25%. So....why can't I enchant that on my rings?

its possible i dunno why you cant dude. You sure you enchant them with -25%destruction and NOT the -15%detruction and +50%regen magicka??? There are two enchants for each magical schools that reduce magicka cost and one can only be applyed on armors

My game on xbox doesn't even show items if I can't apply an enchantment to them, I say something is borked. No idea what however.

This was going to be my guess.

make sure you are using just "Fortify 'School'" enchantment and not fortify school and fortify magicka regen