The reason that I play irelia this way is because it would be a smart idea to take advantage of her natural healing, and more than doubles with a bloodthirster. Which can actually almost let you 1v1 a tower. All the builds I have seen on irelia are oddly tankish and I did not like them at all when I tried for myself. This build has been working for me however. It turns irelia into a better xin zhao, with a stun.