12 year olds are also highly influenced by their parents. It's easy for a parent to threaten a kid to make him vote one way, or bribe him, or just force him to stay in the house on election day if he ever lets his political views slip out. (In theory, a kid could lie in the first two scenarios, since voting is done in secret, but I would bet that a statistically significant portion of kids will be unable to lie well enough to pull it off.)

Also, 12 year olds are less mature than 18 year olds. It may be that the level of immaturity in voters you'll get from adding people ages 12-17 is just too large to be acceptable. (Exercise for the reader: why is 'well, some 18 year olds are immature anyway' not a good response?)

And taking away the vote from demented people and people with low IQ has the problem that the tests may not be perfect. Imagine a test that is slightly biased and unfairly tests black people at 5 points lower IQ. So white people get to vote down to IQ 60 but black people get to vote down to IQ 65. Even though each individual black person of IQ 65 is still pretty stupid, allowing a greater proportion of stupid people from one race than another to vote is bad.