Structure of biological membranes?
Some thoughts on this. First of all, the positive-inside rule, proposed by Gunnar von Heijne, is an empirical rule based upon observations, not one derived from theoretical considerations, so any explanation is simply an attempt at a rationalisation.

Having said that, here are three of those rationalisations:


the membrane potential is usually negative inside. This will create an electrostatic tendency for basic amino acid side chains to stay inside.
most phospholipid head groups are either neutral or anionic (phosphatidylserine, when the phosphate is included). Again an electrostatic force favouring basic residues inside since to move them out would require overcoming their interaction with the negatively-charged membrane surface
the pK values of the basic side chains (lysine and arginine) are much further from 7 than are those of the acidic side chains, so,  since charged residues must be neutralised to get them through the bilayer, it is more energetically unfavourable to deprotonate basic side chains than it is to protonate acidic ones.