You make a very astute point, but I'm afraid it's never as easy as it seems.
I'm not going to argue the ethics of it, because that it basically impossible; I'm only going to deal with the legal side; moral views are left an an exercise to the reader.
On the side of the mechanics of the whole process, here is what I know: In the Unites states of America, voting rights are outlines by 3 amendments to the Constitution:
XV - The right of citizens of the United States to vote shall not be denied or abridged by the United States or by any State on account of race, color, or previous condition of servitude.
XIX The right of citizens of the United States to vote shall not be denied or abridged by the United States or by any State on account of sex.
XXVI The right of citizens of the United States, who are eighteen years of age or older, to vote shall not be denied or abridged by the United States or by any State on account of age.
...and the definitions of citizentry are defined thusly:
XIV All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside.
So, what do we have here? Following XIV, anyone born in this country or naturalized thereof is a citizen, and according to XV and XIX voting rights will not be infringed upon -- but XXVI says you have to be over 18. As a side note, those who are under age of emancipation but were not born on US ground cannot be naturalized until 18, anyway. First point: the precedent is "citizens under 18 cannot vote".
"But wait," I hear you cry, "I pay taxes! Why can I have all of one but none of the other?"
Well. Pursuant statues outlined in US Judicial Code Title 42, Chapter 21, it is stated that persons under age of emancipation are "special cases". The reason why you can work while under the age of 18 is that you are taken as to working under the volition of your legal guardian (an extension of them, as it were). It is also these parameters that frame such things as protection under the law to grant added lenience, to forbid the entering into a legal contract and whatnot. The basic upshot of all of this is that minors are given protection under the constitution, while exercising the executorial rights thereof is delegated as a function of those in legal guardianship.
It may not be fair, but it's like this for a reason. If you give "equal rights" to a certain groups, all baggage must come with it. If you gave "the vote" to "children", you'd also have to make allowances for also giving them mortgages, jury duty, taxes, the death penalty, and removing anything involving the exploitation of children (including the age of consent and statutory rape laws we all think are pretty keen).
It's not just voting that is discriminated by age. In the United States, there is also a statute that states that persons under 18 years of age must attend schooling of some time. This is only viable pursuant to the special status of children. It goes on and on, from that to declaring them a dependants on taxes.
But it's not such a big deal, legally, anyway. The reason is that suffrage in the US is based on attainable attributes, not innate values. What I mean by that is that as soon as you turn 18, *BAM*, you get to vote regardless (providing you register, blah, blah). This is why Amendment XIX is the big deal that it is. Given that I don't die, I will eventually reach the age of suffrage and can therefor vote, and the law can't stop me. However, If I'm female and only males can vote, the chances of me becoming male by any process I can control is highly dubious at best -- it is denying rights based on a factor that cannot/will not be changed.
And that's the difference. If you are a minor, you will probably be 18 soon an will therefor get all the right and penalties that comes with. It's different then saying "you can't vote because you're <ethnic>". This also applies to me: I live in the US of A and I pay taxes, and I'm even over 18, yet I can't vote. Why? Because I'm not a naturalized citizen. But I pay taxes so I should be able to vote, regardless? No, because I can be discriminated against because citizenship is something I could have. I can achieve it, therefor it is not the government stopping me, but other factors -- and once the requirements are met, the law can't stop me.