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Henry Higgins is a man who is blunt in his opinions, who mistreats his furniture, who uses foul language in polite company, and who speaks harshly, at times, to his student Liza Doolittle.
He attempts to justify his behavior by saying:
The great secret...is not having bad manners or good manners or any other particular sort of manners, but having the same manner for all human souls.
In other words, if you act with equal insensitivity to all kinds of people, you cannot be accused of favoritism or prejudice.
There is a certain logic to this. On the other hand, perhaps this statement shows that Higgins is merely self-centered and doesn't care about anyone but himself.