Like a sibling comment says, you risk the baby rolling on to its face and suffocating. All the midwives at the hospital and all the books say to not do it, but any mother in law will tell you to just put the baby on its side if it's fussy. If you challenge the MIL she'll throw the "I've raised more babies than you so I know better" remark in your face. A tale as old as time I guess.

Eventually we caved, and it really works to calm them down. But we only do it under supervision. When she's asleep we'll roll her on her back.

> What's wrong with sleeping on your side?

There's a chance the baby rolls from the side onto their stomach, and that is associated with an increased chance of dying[1].

So in general better to avoid if you can.

[1]: https://www.nichd.nih.gov/sites/default/files/publications/p...