HE-shells contain much explosives and to get space for those explosive materials, shells are hollow and quite thinwalled. That hollow space is filled with HE. Being hollow their structure is weaker than solid shot structure. Hence they cannot be shot with high muzzle velocity which is a key feature on AP-shots. Then again, HE-shells dont withstand the stresses involved penetrating an armour and just break up. This is similar to high velocity problem.
Now, being slower velocity and weaker structure aren't the only reasons. One more reason is the weight. Steel density is about 8 grams / cubic centimeter while explosive density is around 2 grams / cubic centimeter (depending on explosive). Now this means that if you carve out say 4 kilograms of steel out of a shell and put explosives in place of steel, you can put fit only 1 kilogram of explosives. This leaves your shell 3 kilograms lighter than originally.
Now you have a HE-shell that is shot with lower velocity, is lighter and its structure is weaker than AP-shell structure. As higher velocity and higher weight (= higher kinetic energy) are essential to armour penetration, you can easily see why HE-shells are inferior in that.
Of course if you have large enough HE-shell, it probably will penetrate a thin tank armour.
(Disclaimer: not always were HE-shells lighter and with lower muzzle velocity than their AP-counterparts, especially when a gun wasn't high velocity gun. Also high velocity guns might have low capacity HE-shells with thick walls, shot with high velocity.)
AP shells are inferior to HE-shells in bunker busting because AP-shells dont contain much (if not at all) explosives. Bunker busting relies much on explosives, therefore HE-shells are more useful for that role than AP-shells.
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