Mythbuster Matt here,
Word has it that the myth began because a child died after eating a poinsettia leaf in 1919, almost 100 years ago.
It wasn’t until 1971 when researchers at Ohio State University tested the plant’s toxicity by feeding a solution soaked of poinsettia to rats. The conclusion to the experiment was that the rats had “no symptoms of toxicity, nor any changes in dietary intake or general behaviour pattern” even after heavy doses.
You won’t die from Poinsettia, but you could get sick.
Whilst death from consuming Poinsettia has been proven implausible, you could still get sick if you have a latex allergy. When any part of the plant breaks, such as a leaf or the stem, the plant bleeds a latex sap.
Even if you don’t have an allergy to latex, you can still experience irritation.
From experience, I can tell you that although I do not have a latex allergy I have experienced irritation from using Euphorbia. Euphorbia is the genus for the Poinsettia. There are many other plants that fall into the Euphorbia family (pictured below).
I experienced the irritation from using Euphorbia succulent (this last photo). This bleeds in the same way as Poinsettia. If you ever come in contact with a Euphorbia, be careful!