What is ironic about Henry Higgins' language, which is peppered with curses? What sort of teacher of manners and language is he?

Henry Higgins specializes in phonetics, taking Eliza Doolittle and making her his own personal experiment (and wager). Ironically, this master of language leaves his own behavior unchecked...... he curses, and his manners are so atrocious that his mother doesn't want him around when she hosts a gathering. When Pickering bets Higgins that he can never bring Eliza to the point of transformation where she'll pass for a duchess..... Higgins is included in the bet as well...... meaning, he has to improve his own manners and stop cursing.