The layers of onions are the bases of the leaves that once stood green above the soil. The outer layers are old leaves that continuously get replaced by inner, younger leaves. As they die, the oldest leaves return most of their material to the base of the bulb, recycling their resources for the living parts of the plant. Only the “onionskin” remains as protection. The inner layers of the onion bulb are young leaves and buds. They swell as they grow, stretching the outer leaves, and the further out the leaves, the more they must stretch.

Now, onion tissue is made up of cellulose chambers filled with living fluid forced in under pressure, stretching the cell walls, so that the tissue is like a lot of taut balloons stuck together, not flabby at all. Pop some of the balloons, and tension in the rest of the structure pulls it lopsided. Similarly with the onion leaves. The older, outer leaves are stretched evenly, but when you cut off the tops and root bases the outer leaves no longer get stretched lengthwise, only sideways; they shrink elastically, leaving the inner leaves sticking out. A cut at right angles would cause a different pattern of distortion.

As a guess, the external layers of the onion are tight and thus extert a compressive force, so that when you remove the barrier at the top, the insides tend to squeeze out.  It doesn't come out the bottom because onions are a bit pot-shaped.  However you also couldn't avoid squeezing the onion while you prepare it.

Onion is a modified stem, with fleshy overlapping leaves arising from a short stem, covered by papery skin. Inside the bulb, the fleshy leaves—which in some species are actually expanded leaf bases—function as food reserves that enable a plant to lie dormant when water is unavailable.

On tailing and topping the onion, the difference in pressure (Osmotic pressure) between outside and inside of the fleshy leaf cells, some inside fleshy leafs are pushed out with a drops of fluid on the surface.

An onion is made up from concentric layers.  The outer parts are more or less spherical, the more central parts are shaped like elongated cones with the pointed ends at the top of the onion.  It is these parts that form the leaves should the onion be allowed to sprout.  All the layers are joined at the base of the onion so if this part is removed, the layers are no longer fixed in place.  In a fresh onion, there is a significant hydraulic pressure in the layers and the conical inner parts are squeezed out of place - as seen in the picture.

I have notice this too, and also that the longer the onion is left uncovered that the core almost will pop out of the onion.

I have always assumed that it is due to the loss of moisture, that happens from the minute you remove the skin.