Specifically what is wrong with teenage pregnancy? I've never understood the shame that is associated with it the West. The vast majority of arguments that can be made against teenage pregnancy can be made against single mums, yet we seem to celebrate them if anything (at least here in the UK).
Having kids is one of the most selfless and rewarding things someone can do. While I agree economically it would be preferable to encourage people not to have kids and to focus on careers instead I struggle to justify using this as a reason to discourage people from having children.
That said, I suppose the financial situation of the parents could be a factor here depending on the country. Generally teenage parents won't have very high income, but in the UK this wouldn't be an issue. One of the primary reasons women in my family have kids young is for the financial security. Here in the UK having kids is one of the best paths to moving out of your parents home in your 20s if you're from a working class background. But again, this financial argument applies in many other situations. Should single mums not have kids? Should people who can't work because of a disability not have kids? etc...
The only other reason I've heard is that teenage parents are too immature to raise children. I don't accept this. The easy argument to make against this is that there are plenty of immature people among my family and friends who have kids. Many of whom do drugs and are generally not great members of society. These people have never been discourage by the state not to have more kids. There are lots of very mature teenagers who can raise children just fine. But I'll accept this is more subjective and nuanced position which I'll need to defend, and I'm happy to do so if necessary.
I guess could someone just give a good argument against teenage pregnancy? Ideally one argument that doesn't rely on your subjective values about what a fulfilling life involves? I'll note that I'm talking ~15+ here. My understanding is that there could be pregnancy complications younger than this, although I'll add this applies to older individuals too where I believe similar disincentives should be applied (40+).