Are there chemicals in toothpaste that can hurt you?

and...

Why can’t you swallow toothpaste when you can swallow a mint?

It is not recommended that you swallow toothpaste. This is why children under 6 are not supposed to use toothpaste.

The main bio-active ingredient in toothpaste is sodium or tin fluoride. A tube of toothpaste contains enough fluoride to kill a 6 year old, and since toothpastes can come in flavors like bubble gum or watermelon, they should be kept away from young children. That said, few problems are actually reported, and the problems have not been fatal, even when severe.

Fluorides can damage the lining of the stomach, and usually cause nausea, whereby most of the toothpaste is eliminated and not absorbed into the bloodstream.

Toothpaste for young children does not contain fluoride, and is safe to swallow. Since their teeth are temporary anyway, the lack of fluoride is not  a long term health problem.