Because you're not a parent, here's a tip: kids are tougher than you give them credit for and they're tougher than they understand. Your responsibility as a parent is to figure out how to toughen them up without crushing their self-esteem.
Instagram is not an essential part of any of this. If the worst thing your kid can say about you when they hit adulthood is "daddy didn't let me on Instagram," then you did a phenomenal job.
You're missing the point. It's not "Dad didn't let me on Instagram". It's "Dad didn't let me have shared experiences to build relationships with my peers."
To be fair, it’s a 50/50 shot whether your high school peers turn out worthless or not. For the children of the HN crowd, I give better than even odds that their real lifelong friendships won’t be formed until college.
If a shared experience is toxic to the mental well-being of my kids, then they're not going to share in the experience. I'd rather my kid hate me for a couple years as a teenager for not letting them engage in harmful things than never getting out of their teenage years.
Instagram is not an essential part of any of this. If the worst thing your kid can say about you when they hit adulthood is "daddy didn't let me on Instagram," then you did a phenomenal job.