Some people are very heavy sleepers and might not notice turning over onto their infant.
Additionally, the other big reason that you're not supposed to have an infant sleep in a normal bed is that they might roll off. It's fine I guess if both parents are around and "box" the infant in, but otherwise it's quite possible that the infant might toss over one too-many times and fall off the bed.
I replied in detail downstream, but as I've said there too, parenting is a personal thing, and I am not out to convince anyone one way or another. I was just amazed at what I read when I bothered to do the research, and it didn't seem too scientific (baby with meat cleaver in bed poster by Milwaukee Health Dept. [1]).
I'll repeat myself a bit here by re-quoting this article, because I think it's important.
"The United States has a higher infant mortality rate than any of the other 27 wealthy countries, according to a new report from the Centers for Disease Control. A baby born in the U.S. is nearly three times as likely to die during her first year of life as one born in Finland or Japan." [2]
Co-sleeping is not the reason for those rates, and if it were it would be more embarrassing for the US, since other countries don't seem to have the same results.
I am from the US. I had my first child in 1997, and my latest in 2014. I am now living in the East Java, Indonesia in a rice-farming village where most of the house have dirt floors. I have raised a kid in NYC, NJ, and now here. I am more worried about King Cobras than co-sleeping risks, and fatal bites are very, very rare for non-snake handlers or performers.
And for the record, I don't like the term co-sleeping; I prefer to say we have a family bed ;)
We've occasionally brought our little dude into bed with us when he's going nuts, but also know the potential consequences. It's not generally safe to bring a child into an adult bed and I know without my spouse being super-vigilant I might roll over onto him.
Additionally, the other big reason that you're not supposed to have an infant sleep in a normal bed is that they might roll off. It's fine I guess if both parents are around and "box" the infant in, but otherwise it's quite possible that the infant might toss over one too-many times and fall off the bed.