Higgins is what you might call a bundle of contradictions. He's a woman-hating mama's boy; an incredibly talented, educated whiny little baby of a man; a personable misanthrope; a loveable jerk. The only thing he's not is...easy to pin down.
Shaw says it best in his initial description of Higgins:
His manner varies from genial bullying when he is in good humor to stormy petulance when anything goes wrong; but he is so entirely frank and void of malice that he remains likeable even in his least reasonable moments. (2.05)
The first time we meet Higgins he's acting as a combination street magician/peacemaker. He calms down Eliza, then proceeds to show off his skills by telling people where they're from just by listening to the sound of their voice. Oh, and he can mimic them too. Right from the beginning we can tell he's a bit of a braggart and a bit of a preacher—he can't help but tell Pickering all about his trade, his life philosophy, and his ability to turn flower girls into duchesses just by changing their accent and speech pattern—but as far as first impressions go, he makes a pretty good one. He comes off as a cool customer.
By the end of the second act, things have become more complicated. It turns out he treats women like trash sometimes, and his motives for taking on Pickering's bet seem less than sincere. He begins bossing Eliza around rather quickly, telling her what to do, manipulating her with big promises and chocolate—he can tell a chocoholic from a mile away, you have to give him that. He even pays Eliza's father so that he can take her into custody. All of this happens before he calls her an idiot and a slut and almost assaults her…twice.
Higgins's actions spring from some unexplained distaste for young women, who he tells his mother are "all idiots" (3.23). Oh, and he has this weird thing for women that remind him of his mom. At various points in the play he compares women to blocks of wood, calls Eliza garbage, asks to have her wrapped in brown paper like a package, and refers to her as "his masterpiece."
Both his mother and his maid, Mrs. Pearce, point out how unfair this all is and how, in Mrs. Pearce's words,
You can't take a girl up like that as if you were picking up a pebble on the beach. (2.101)
Though he can be a stubborn jerk, Higgins is definitely not a fool. He knows he's a jerk, and he's even come up with a justification for his behavior. After Eliza accuses him of treating her unfairly, he tells her,
The great secret, Eliza, 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 short, behaving as if you were in Heaven, where there are no third-class carriages, and one soul is as good as another. (5.197)
This is the best example of Higgins's high-minded, philosophical side. Sounds pretty convincing, right? Thing is, sometimes it's hard to tell if he's really being sincere or if he's just trying to get out of a tough spot.
He does, however, have a penchant for talking about the soul of man, about the importance of language, and social equality. Given Shaw's socialist leanings (he was a member of the British socialist group, The Fabian Society, and wrote on and debated various social issues—learn more here) it's hard to dismiss everything Higgins says as meaningless claptrap.
Higgins's fervor can get him into trouble, however. He spends so much time "inventing new Elizas" with Pickering that he seems to sometimes forget that she's a human being (3.230). He forgets to congratulate her for her bet-winning performance. He gets so angry he nearly hurts her, and he ultimately puts her into a very tricky position.
Talking all this into consideration, it's hard to pass judgment on Higgins. He's always likeable, sure. He's the play's voice of reason, the preacher and poet, but he's also a slovenly, absent-minded troublemaker. He is the engine that drives the play. He's not Mr. Perfect, but he has heart.
He's also the closest thing we get to Shaw, but don't make the mistake of substituting one for the other. Higgins is like Shaw in some ways, but he is not Shaw. He's Pygmalion, the character, and it's safe to say that he's also Pygmalion, the play. Without him, the play just couldn't exist.