User blog comment:Xxace77/Zoro's right eye foeshadow?/@comment-3242083-20110822155240/@comment-76.118.242.65-20120419211910

the only two reasonable theories are (1) closing his eye to handicap himself against weaker opponents- the scar is not too deep but it makes for good fan debate and interest in why his eye is closed,

or (2) he gave it up to mihawk in exchange for the training. I do not think mihawk would take his eye as he told zoro "training will begun once youve healed" and smiled pretty happily. It is said many times he is just "killing time" and it implies he has been waiting for a swordsman strong enough to challenge him, he sees that in zoro and prob would not want the advantage of a big blind spot on zoros side.