It's a well known (scientific!) fact that children grow and learn. At some point, they stop growing, and, well, slow down in learning. At that point, they become adults. Children cannot consent. Adults can.
There are a couple serious problems with this approach.
1. Not everyone "stops growing" at the same age. How do you determine whether or not someone has reached that point yet, using nothing but pure logic?
If you have a good answer that can be practically implemented, then I'd honestly love to hear it. I personally oppose age-based laws as a matter of principle, because I believe discriminating against someone because of the specific number of times they've orbited the sun is every bit as unfair as discriminating based on the color of their skin. But the alternatives I've heard are far from perfect. I think they'd still be better than age-based laws, but I accept that they'd involve a lot more false positives, which is fine with me - that's a matter of priorities (I think giving young people freedom is more valuable than protecting them from the consequences of their own choices), not logic.
2. "Children cannot consent. Adults can" is an awfully simplistic and glib way to talk about it. Children can and do consent to things every day: for example, no one seriously argues that a 10 year old can't make an informed decision between chocolate and vanilla ice cream. What people claim is that children lack the capacity to make informed decisions about some things which have particularly dangerous or permanent consequences, or which require some (vaguely defined) sort of life experience or "emotional maturity" to be truly informed.
There is no "consent" section of the brain that suddenly comes online on a person's 16th or 18th birthday. There is no bright line between "child" and "adult" at a biological level. There is no scientific consensus, let alone logical proof, as to what physical capacity a person needs to make informed decisions, or how to measure that capacity, or even at what age that capacity tends to arise (see the variation in ages of consent across the US and around the world). Setting a policy here requires more than just logic.