I think I disagree - there probably isn't, really, a fundamental, entirely-logic-based way to decide 'the truth' regarding at what age one attains adulthood with the ability to make adult choices. It's always going to be a culture-dependent question (though I suppose improved scientific knowledge about brain-development comes into it a bit).
And hence it's commonplace for such arguments to involve references to the inconsistencies we have about the topic. E.g. here it used to be allowed to join the army (and even, at one time, be sent into combat, though that changed at some point) at 16, while you couldn't vote or buy alcohol till 18 (but you could consent to sex at 16). People noted that was a bit inconsistent. Generally the trend, though, has been to slowly increase the age for 'adulthood' for most things, but there's always been an odd-mishmash of age-cut-offs and I don't think it's fallacious for people to argue there should be some consistency there.
Its nice to see someone that gets it. If a system for judging things causes inconsistent outcomes, then maybe the system should be examined. Does not invalidate anything directly, but, it seems reasonable to examine the framework.
Signing up to die at 16 and limiting alcohol until 18 seems inconsistent at face value. You are disallowed from comparing them because they are different by the rules of smog.