What? Latex gloves are water proof. Where can I learn more about the chemicals impregnating the gloves?
Your hands will be at least a little damp and soapy. How did that happen, if latex is waterproof? It's because your hand doesn't make a perfect seal with the glove.
Also, dish soap and other detergents are surfactants, which reduce the surface tension of water. That makes it easier for it to get into tight spaces, like the space between the glove's edge and your hand.
Finally, latex is soluble in many kinds of oil/petroleum-containing product (many waxes, some heavy-duty cleaners, etc.), so if you're wearing latex gloves, you'll literally be dissolving latex onto your skin and degrading the gloves. Gross.
If that's what a three-second test will do, imagine how it'd feel to wash clothes for thirty minutes. Not pleasant.
Trust me years ago I worked on on project that was simulating a nuke reactor (the CFR breeder) and had to spend an afternoon wrapping a dummy fuel pin with insulation in full bunny suit, respirator and latex gloves on a very hot day when I took the gloves off there must have been 50 cc's of fluid in the gloves finger tips.
No, it's because your hands generate sweat, which cannot evaporate due to being completely sealed in by the latex.
Here's a test for you: fill a latex glove with water and see if it is leaking any. You will see that it is completely waterproof.
The soap got in through the edge of the glove, not through the glove. Your test won't demonstrate anything other than that latex can hold water, which is not what I was trying to show.
I wasn't kidding when I said to try it. :)