While I disagree with this person's view, it is certainly not as radical as it appears. The government, through many different agencies, tempers both what the youth can say, as well as what they can hear, see, read, do, etc. The logic behind the restriction of free speech for those under 18, is that they are not developed enough to fully understand that to which they are being exposed. What is the difference between a 17-year old kid in high school and an 18-year old kid in college?
That said, I do not think this guy is being consistent in his thoughts, insofar as he neglects the issue of voting. If you are going to argue that free speech ought not apply to certain individuals due to their lack of mental development, then you must also argue that they should not be given a vote due to their lack of mental development.