Setting the voting age at 25 would be a sure fire way to destroy young people's prospects in this country. It's bad enough that we have things like the tuition fees debacle, where not one person affected by that change was old enough to vote in the election that gave rise to it. Imagine how much worse that would be if we disenfranchised young people for another 7 years.
If the voting age were set at 25 I would not actually have had the opportunity to vote in a general election until I was 29, nearly 30. By that age I'd been a higher rate taxpayer for a couple of years and was trying to buy my first home (unsuccessfully, in the end). I had friends my own age who were working as doctors or running their own businesses, some had bought homes, some were married, a few even had children. My best friend from school was a married mother of four who had been working full time and paying taxes for over a decade by that point.
The only thing that is set at age 25 in this country is that if you look like you could be under that age you have to be ID'ed when buying alcohol, and frankly even that is ridiculous.
The argument that people's brains don't finish developing until they are 25 is, I think, valid when talking about major and irreversible life decisions affecting the individual. I understand why, for example, some trust funds don't pay out until the beneficiary is 25. I think 25 would be a more appropriate minimum age for gender reassignment surgery. But an individual person's vote changes very little. No individual is going to fuck their life up, or even the country up, by voting the wrong way. And if your argument is that only people who can be trusted to vote sensibly should be allowed to vote, it seems pretty arbitrary to say that no 16 year old should be allowed to vote when many of them are clearly capable of voting sensibly, whilst ignoring the fact that 50 year olds can vote and many of them don't vote sensibly.
We don't give sensible people the right to vote as a prize for being sensible. We give people the right to vote because they have a stake in the future of the country and have a right to participate in democracy. I don't see why that principle shouldn't apply to 16 year olds. Of course you have to draw the line somewhere but I don't find 16 any more unreasonable than 18. And about a quarter of those 16 year olds wouldn't actually get to vote in a general election until they were 20 anyway.