I think a lot of it is reactionary. The opposite is also true, what used to be shocking and scandalous a few decades ago is commonplace and acceptable now.
The poles keep drifting further away from each other and society is increasingly divided between them.
Age of consent exists because young humans are ridiculously easy to manipulate and take advantage of, especially by an adult. It's not that 14 year olds don't get horny or their junk doesn't work, rather they are vulnerable to abuse and so these laws exist to try and protect them.
Almost universally, people don't want anyone fucking their children until they're certain that they are old enough to make informed decisions.
I don't think the punishment necessarily fits the crime here, but it's not a simple taboo either.
When it comes to sex, most countries legislate against the age difference, not so much the act itself. If it's two 15 years olds doing it together then the law doesn't care in most places. The law does care if one of them is 20 though. There's a huge power imbalance between a 15 year old and a 20 year old, the 15 year old doesn't have any real life experience to draw on either, so they are vulnerable to abuse.
Teenagers are stubborn and think they know everything - this is absolutely true, call that headstrong if you will. They are also at the mercy of hormones, tend to be emotionally unstable, don't have any real life experience yet, are idealistic, rebellious, etc. Throw in the inherent power imbalance between them and an adult, and I maintain that they are really easy to manipulate and take advantage of.
I think we can both agree that the line has to be drawn somewhere, you just believe it should be lower. Indeed countries around the world aren't aligned on it either, the age of consent is 16 in some places, 18 in others, some even higher, etc.
Some things are outright silly, for example I strongly disagree with having to be 21 to buy alcohol in the states, I think that's just stupid. In places like Belgium the legal drinking age is 16 and to me that feels right. Teenagers are going to drink no matter where you set the bar, driving it underground helps nobody.
I also see no problem with two 16 year olds getting it on. I absolutely think it's problematic for a 25 year old to be chasing a 15 year old though.
Personally I would define it based on the age gap, e.g. it's not a problem as long as the age gap between them doesn't exceed 2 years while one of them is under 18. All bets are off after that.
Drinking legally I would set at 16, voting and joining the army at 18.
Yes we can watch a short documentary with moving music and touching narration about how the life of this poor young mother is ruined because she had consensual drunken sex with a minor. There are also countless examples of grown adults preying on young teens for their sexual gratification. At the end of the day, nobody wants that to happen to their child.