Somehow I put a lime egg into a red egg, with the intent on putting all my eggs in one egg to just clear up some space, but the others ended up being too heavy, and actually couldn't put any other eggs in eggs. Tried to pull out the lime egg from the red egg, and the red egg disappeared.
edit; the spinoff issue appears to be when placing the egg on the ground and trying to put another egg inside it that way. Masterdevil (at the result of a major misunderstanding, which has since been deleted) had seemed to confirm that you can place an egg inside an egg if it's in your inventory, where my issue came up was when trying to put an egg in an egg that was placed on the ground. I was able to place a lime egg into a red egg in this way, but the others I've tried all say "this is too bulky to fit in that"… not really in a hurry to test this with all of my eggs cause I would like to keep them, since "opening" the egg apparently causes it to disappear. This gave me the impression I wasn't actually allowed to place eggs in eggs, but apparently you can in one way but not the other (sort of?), and it's not a good idea if you want to keep them… At any rate, this at least helped narrow down what exactly I was experiencing here, and that this isn't exactly working uniformly.