Question: why is yuuki stronger than kirito?
Answer: Yes Yuuki is stronger then Kirito, Word of God says he might have beat her if he used two swords with one of them being Excalibur but that would be pretty much Kirito simply out gearing her. ... In a duel Kirito isn't as serious and will stick to single sword and will be beaten most times (if not all) against Yuuki.