Take a bag, fill it with water, and grip it loosely at the top so all your fingers wrap around like a loose fist.
Now, without turning the bag, use your other hand to empty it by squeezing out the water.
You get most of it out, but there's still some in there, even if you squeeze violently and it seems like nothing else can come out.
Also, for most of human history, if you've poisoned yourself ingesting something, chances are the next thing you're ingesting is still poisoned. It's only recently we've worked out distilled poison and purified water. So, biologically speaking, better to just be sick for a day so you can get to a different water/food source.