Kata invoke some strong feelings. Many competition oriented martial artists consider kata training a waste of time. Many koryu bugei folks think competitors miss all the important lessons, and Ueshiba Morihei, the founder of aikido, proclaimed there are no kata in aikido.
What are "kata" that they generate such strong feelings and statements? They are just pre-arranged movement patterns. In budo, they are pre-arranged patterns for movement for dealing with conflict. In Japanese arts, with the exception of iaido, they are always paired practice. Since iai deals with handling a live blade, it would be tough to keep finding new partners after every mistake, this makes a certain sense. But what is being studied in these kata, and why kata instead of free sparring. After all, kata was the dominate teaching methodology for budo in Japan until the 1900s. And what was it about kata that made it strong enough to be successful against styles that emphasize randori (sparring) and in live matches for hundreds of years. It's still the dominate training method for most koryu bugei.
Kata must have something, because extremely successful systems like Yagyu Shinkage Ryu kenjutsu are all about kata. Yagyu Shinkage Ryu consists of 22 kata, through which the whole of the kenjutsu system is taught. What's going on here that an entire school of sword fighting can be boiled down to 22 forms?