I don't find arguments against letting children vote very convincing either, except the argument that 18 is a defensible Schelling point and it would become way too vulnerable to abuse if we changed it to a more complicated criterion like "anyone who can give informed consent, as measured by X." After all, if we accept the argument that 12-17 year olds should vote (and I'm not saying it's a bad argument), then the simplest and most effective way to enforce that is to draw another arbitrary line based on age, at some lower age. Anything more complex would again be politicized and gamed.

But I think you're misrepresenting the "influenced by parents" argument. 22-year-olds are influenced by their friends, yes, but they influence their friends to roughly the same degree. Their friends do not have total power over their life, from basic survival to sources of information. A physical/emotional threat from a friend is a lot less credible than a threat from your parents, especially considering most people have more than one circle of friends. The same goes for the 75-year-old - they may be frail and physically dependent on their children, but society doesn't condone a live-in grandparent being bossed around and controlled the way a live-in child is, so that is not as big a concern.