The idea that sex is inherently soul-breakingly harmful in all people right up until some uncertain point around age seventeen isn't really something I'm completely on board with in terms of true things about individuals, but it's useful as a rule for sure.
What I am pretty **** certain about, on the other hand, is that our culture has some messed up ideas about sex at the best of times, and it's so deeply ingrained that opting out really isn't an option. Trying to deal with that crap as a child is pure hell, especially when there's so much other stuff kids are already trying to figure out about themselves and the world around them. Some of which, coincidentally, is vitally important for healthy sexual activity at any age, let alone when you're dealing with it all for the first time, and you've got no real experience helping you distinguish between good information and bad information.
I mean, you don't even have to start thinking about coercion or violence, or (perhaps hard-to-grasp) concepts like informed consent; just the decision to have sex, even when you feel as if you're completely in power over it, is heavily steeped in complex ideas about identity, and aggressively shaming rhetoric. Imagine trying to deal with the entire world telling you, simultaneously, that you're young, so you're a child, you're innocent, you're free to try new things and figure out who you are without worrying too much about any particularly life-changing consequences - but you've had sex, so you're an adult, you're a slut, you're worthless, that your life will go nowhere and you're personally responsible for every bad thing that ever happens to you. It's usually at least somewhat subtle, but this recent contraception debacle has lead to a lot of popular, influential voices being surprisingly frank and overt with their slut-shaming. I think you're familiar with feeling alienated and isolated from your peers, or the feeling that you've betrayed everyone you love. Is that really something you want to inflict upon a child?
But it's not even that simple. In the real world, complex power dynamics are an unavoidable aspect of all relationships. Your decisions are influenced by feelings of obligation and subconsciously expressed pressure. Religion is often seated pretty deeply in a person's heart, and they tend to have all sorts of things to say about sex and sexuality. The result is a powerful and complicated mess that's near impossible to successfully navigate when you're a fully-grown person; it's normal to have a few problems, but most adults have the resources to deal with them. A strong sense of identity, a firm grasp on your sexuality, or a kind and trusted support base with whom you can talk about anything. Children are exceptionally lucky to have a single one of these, and even then, they're often unstable and impermanent. A relatively small issue for an adult can cripple a child for the rest of their life, simply because they didn't have any way to defend themselves from it.
Honestly? I was kinda like your friend, once. It wasn't immediately obvious to me why sexual activity is categorically a bad thing for young people. I did have to spend some time thinking about it before I really understood, and could confidently give an explanation that satisfied me. Even at my moments of vaguest doubt, though, I never thought that it would maybe be OK to allow in some cases, simply because of the sheer risk involved, if I was wrong. You'd basically be gambling with a person's life, and for what? A little sexual gratification? Is that seriously a worthwhile risk to take, regardless of what the result turns out to be? It'd be like making someone else play Russian roulette so you could maybe win £100. The risk far outweighs any possible reward. Even if you managed to "win", nobody dies, and you get your £100, it was a monumentally stupid and psychopathically careless thing to do, and you should never have done it in the first place.
Obviously there's a mountain of other reasons, but I thought these might be useful for where you currently are. For your anxiety... Well, I'm not really sure how people deal with anxiety, per se, but if you're trying not to think about children, maybe find something else to fill your head with? Memorise a song, or a picture, and really focus on reciting and remembering every single detail of it in your head. Try slipping a hand in your pocket and pinching your leg really hard, and focus intently on the pain. Really, being able to control your focus seems pretty important - aren't there exercises you could try, to help improve it? Stuff like picturing one thing in your mind, and thinking about nothing else for as long as you can. Stuff you can practice on your own, when you aren't having to worry about being around children. A lot of the lessons involved in learning how to meditate seem like they'd be reasonably applicable, maybe you could look some of that stuff up. Not sure what you have and haven't tried already, sorry if I'm just saying stuff you've already looked into.