Then why not start women's voting age at menarche?
I am tempted to just flip this around. You mentioned experience and the maturity of the brain. Why not reserve voting privileges for senior pensioners. Their brains are all grown and they have the most experience, as well as endless time on their hands.
You probably meant it as a ridiculous question, but even though I would not propose letting 10 year olds vote or that young voters should bring a doctor's note to the polling station, I think it is a question worth thinking about, because the body (the fertile female body in particular) is heavily contested political territory. We as adults need to acknowledge the responsibility of making decision of behalf of young people with limited autonomy and control. We take the role of their (supposedly) benevolent caretakers when we decide matters such as availability of contraception, abortion rights and possibility of gender correction surgery or treatment.
If we raise the voting age to 25 (sic!), then the belated response of the governing body to the will of the populace will ensure that the votes of you and your peers won't matter until you are entering middle age. By this time, the child you could not abort at 16 has grown up and left the house, you chose to have no more children, because kindergarten was too expensive, and your same sex partner of 10 years died in hospital, but you could not say goodbye, because their family denied you access. Of course, there is a lot left of life, but what do you really need politics for now? The benchmarks of your life have come and gone and things turned out like they did. You've almost paid down the mortgage to your flat, so financial security will ensure that you can handle most future eventualities. All your vote is good for now is tyrannising the young.
Setting the voting age to 25 would create an underclass of young people. Seniors would be free to raise income tax and lower property tax, and ensure insane pensions for public servants. As mentioned by others, during the Brexit referendum, a high number of seniors voted on a decision that would have little bearing of their own lives, but which is likely to be a turning point in the history of Britain, Europe and the wider world. Many young people chose to stay at home, which is there prerogative, but imagine if most of the people who would actually live to see the full effect of the referendum were barred from having their opinion even heard. What old person would care about climate change or renewable resources? They're on their way out and their grandchildren don't visit anyway, so let's buy a summer house somewhere warm, so we can bring home some exotic diseases in our poorly resistant bodies.
I think there are three things worth considering when deciding when people should be allowed to vote.
1) People should be able to have a say in matters that concerns them. People in their twenties are in an important stage in their lives and they are important to society. They have to both start their careers and establish families.
2) There should be some balance between rights and responsibilities. We cannot infantilize people in their early twenties, and neither should we lord over them. Children and young adults under 18 (here and most elsewhere) do not have the same rights as legal adults, but neither are they responsible for themselves in the same way.
3) The last would be the ability to form a political opinion. I am not a rationalist and lean quite far towards post-modernism, so I don't give this too much weight. For me, truth is very much a power issue. I don't think rationalism or democracy really work together. I would assume a radical rationalist would prefer a system like the one Plato lays out in The Republic, where a trained elite of the best and brightest form a ruling class. Surely, if we were serious about
ability to vote, we would also bar the mentally challenged and ill informed from voting. Democracy ensures that the country is run in a way that alienates and upsets the fewest amount of people, thought there are places where it has failed spectacularly, such as in Norther Ireland, though they have been somewhat successful in ensuring minority participation.
TL;DR: I am happy with 18 as the voting age, but I would rather see it lowered than raised. If the alternative was raising it to ... say 30 ... I would rather let toddlers vote.