The reason you're not supposed to swallow toothpaste is because swallowing toothpaste can lead to fluoride poisoning.
Toothpaste is safe to brush your teeth with but when swallowed the toothpaste can be poisonous and could cause illness.
It's unlikely that you would die as a result of swallowing a bit of toothpaste as it takes more than a small amount of toothpaste to get poisoned.
I have accidentally swallowed toothpaste before but only a small amount and what happened was I got a stomach ache.
However the stomach ache went away within a few hours.
It would usually take at least 1 tube or 2 tubes of toothpaste being swallowed before you actually got sick enough to die.
But still always spit out the toothpaste when done brushing your teeth as toothpaste is not meant to be swallowed.