There are two threads with which to tackle the issue of youth rights, and in this post (and part 2) I will take on one of them: What makes youth qualified to vote? This question cannot be answered on its own, and so instead I will attempt to address the following:
What makes anyone qualified to vote?
Voting is the fundamental role of the citizen in representative democracy, by which continued governance earns or loses consent, and so were are going to assume that citizenship is the requirement for an individual to vote. Citizenship entails many things, but the important one here is a vested interest and stake in the governance of a nation. This stake can be represented as taxes, but is not limited to involuntary (though consensual) financial contributions.
Citizens, as affected by the actions of government, have a right to deny consent (to the specific actors and not the whole system, generally; but the second amendment is in place for the latter concern). People are granted this right through either deliberate action on the individual's behalf and then granted on completion of that action, as in the case of legal immigration, or by right of birth in the nation and then granted on attainment of a certain age.
Granted is not really the word to be using here; the right to vote is earned. It is clearly earned in the case of immigration, where we have tests and lessons and a whole process of citizenship in place. Earned is harder to pinpoint in the case of voting rights granted upon attainment of 18 years of age. This is granted/earned on the assumption that 18 years is enough time spent to learn and to understand the rules and traditions of this nation, and the assumption that an 18 year old is responsible enough to grant or deny consent to government.
Rights of citizenship, once earned through formally earned (or aged into) citizenship, is taken away in few circumstances: deliberately changing one's citizenship to that of other nation, being convicted of a felony, engaging in open rebellion/armed conflict against this nation. Rights of citizenship are denied when one clearly does not value or hold to the laws of the nation, and so the rights are taken away when a person exempts themselves from organized society.
What's important here is not so much when rights are taken away, but when they are not. Rights are not taken away for other cases of bad judgment (misdemeanors), deteriorating mental capacity (senility, Alzheimer's, or other such circumstances). Rights are taken away when a person decides they don't want to be a citizen, or act in such a severe manner as to prove citizenship is meaningless. Rights remain so long as the citizen does not knowingly and willingly forfeit them, even if the citizen shows remarkably poor judgment in executing those rights.
The National Youth Rights Association points out several examples of people older than 18 but not formally denied the right to vote, but I think the distinctions can come across as arrogant and off-putting. Yes, the mentally disabled are not barred from voting while teenagers are, but saying that can lead to the disenfranchisement of another segment of the population (who, yes, isn't voting in numbers significant enough to constitute a constituency) as easily as it can lead to expanding the vote to teenagers. Also troubling, it could lead to medical diagnosis being a valid way to remove the vote from people.
That is of course the opposite goal of anything that seeks to expand the franchise, and so standards of competence, besides those already contained in our notions of earned citizenship, are not helpful. The question now moves from "why are citizens qualified to vote" to "why aren't teenagers full citizens".
Using "full citizens", I'm acknowledging the rights already conferred to teenagers that are commonplace (drivers license before citizenship), that are institutional (some rights conferred to those currently in public school), that run into tricky child/adult labor regulations (workers permits, right to get a job at some teen year), and rights that come into conflict (parental responsibility and authority/teenage emancipation). There are many conflicts here, and as far as I know (which is some knowledge, but I will be the first to say I'm no expert on these matters), a lot of this is uncertain as it varies from state to state, while the vote (and citizenship) at 18 is a national law. (side note: The constitution also contains other age requirements (and requirements of time lived in the nation) as requisite for holding elected office, so age is something we associate with suitable judgment and experience in this country is something that bestows the right to have a say in this nations affairs.)
The gray areas are interesting, and are the key to understanding youth rights. They'll be the focus of the second post, but before I go into that, one final case study is needed here, about the last time the voting age was lowered
Voting at 18 as national law was instituted in 1971, and it was tied into a fundamental role of citizenship. The draft was for males 18 years and older, but at the time there was no set national voting age (as the matter was constitutionally left to the states), but the standard was 21, and some states placed the bar higher. Lowering the age to 18, and making a national standard, served as a politically expedient way to counter cries of "old enough for fightin' but not for votin'", but besides bitter realpolitik, the rationale meant that if one is going to, as citizens duty, fight a war in the national military, one should be able to consent (and withdraw that consent) through voting. (Also worth noting, the United States is a democracy where the active-duty military is allowed to vote; some nations don't go for this, but I think we're fortunate to live in a state where the people fighting a war can vote to support or oppose the officials who sent them into war.) More important in the matter of voting at 18, no matter how calculated it may have been as a draft age, it now means that the government acknowledges that 18 year olds have sufficient stake and interest in the nation to both die in its wars and elect its leaders. The have this stake even if deemed unfit for military service, as being eligible for the draft is all it took to make people eligible for the vote.
Still, there's a curious exception to the draft age at 18. In the United States, youth 17 years of age can join the military, with written parental consent. These youth cannot yet vote, so the citizenship that matters here is that of the parents, and the distinction between rights inherent to the parent and rights bestowed on the youth. This will be the focus of post 2.