Why did romans think it was important for their laws to be written down?

First of all, the number of the tablets are unimportant. "The Twelve Tablets" refer to the corps of Roman laws that were enacted. It could have been Six Tablets or Sixty Tablets, it just happened that the Roman laws fit on Twelve. The important thing about them is that they were written down and everyone could see what was legal and what their rights were. Previous to this, justice was dispensed according to tradition and that tradition could and often was interpreted to favor the wealthy.