I tried to disenchant http://elderscrolls.wikia.com/wiki/Boots_of_the_Old_Gods
However, there is no such option. The item isn't listed even though it's on my inventory.
Can I or can I not disenchant those old gods items, and why?
This one says http://www.gamefaqs.com/boards/615805-the-elder-scrolls-v-skyrim/63242152 that it cannot be disenchanted. I have no idea whether it's true or not. If it were true, I have no idea why.
Boots of the Old Gods should allow me to learn fortify sneaking I think.
Best Answer
Many unique items cannot be disenchanted and the wiki you reference in your question is correct in saying that Boots of The Old Gods are one of them.
Infuriatingly this convention of items being unable to be disenchanted is somewhat arbitrary, as the ring of the beast has the fortify unarmed enchantment, but may not be disenchanted, while gloves of the pugilist have the same enchant but can be disenchanted.