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When you're applying force to the ends, the force is distributed more evenly over the whole eggshell, because of the way that its kind of pointy at the ends then there's a gradual gradient outwards and back in, but if you crush it from the sides there's not enough gradient in the curve to distribute the force evenly throughout the shell. Hopefully that made sense.
Or, the ends act kind of like an archway but in 3d, very strong, the sides are curved too yes but its easy to imagine that an archway that is barely curved is going to be alot weaker than a proper archway
There is also the issue of symmetry.The curvature in two planes is not the same when squashing an egg on its side and the stresses are different. There is a very large curvature in the 'end to end' (North South) plane compared with smaller curvature in the 'Equatorial Plane' so the stress is not shared equally. On end, the arrangement is symmetrical and the stress is shared equally in all directions.
This more of a Physics / Technology question, really.