What makes the communication between Higgins and Liza difficult in Shaw's Pygmalion?
The simple answer to why communication between Liza and Henry Higgins is difficult is "her dialect" and "his overbearing, pompous attitude"! However, we'll try for something more useful. Liza is poor, was raised in a village called Lisson Grove far to the west of London, and had only the most basic education. Therefore, with all these factors combined, she speaks in an English dialect that is an extreme version that never yielded to the influence of the standardizing London dialect.
Ow, eez ye-ooa san, is e? Wal, fewd dan y' de-ooty bawmz a mather should, eed now bettern to spawl a pore gel's flahrzn than ran awy athaht pyin. Will ye-oo py me f'them?
Translated to a standard English pronunciation, this means: Oh, he's your son, is he? Well, if you would have done your duty by him as a mother should, he would know better than to spoil a poor girl's flowers and then run away without paying. Will you pay me for them?
Professor Hggins is a gentleman, meaning he is from the privileged ed classes, and therefore used to having no obstacles in his way. He is an expert in his field, which he views as a highly prestigious one, and linguistics is in fact rather a high prestige academic study. He has the personality of a bull dozer and, as his mother says, speaks his mind freely without consciousness of the affect he has on listeners. For both these reasons, Liza and Higgins have a difficult time communicating.