In Pygmalion, Alfred Doolittle is Eliza's father. With the character and values that truly mirror his compound name containing the words "Do" and "Little," it is no surprise that Doolittle boasts with this statement. Let's look at a little bit more what he says in Act II with a certain "gift of rhetoric" that eventually gets him in trouble:
I ask you, what am I? I'm one of the undeserving poor: that's what I am. Think of what that means to a man. It means that he's up agen middle class morality all the time. ... I don't need less than a deserving man: I need more. I don't eat less hearty than him; and I drink a lot more.
Considering he finds himself "undeserving, and I mean to go on being undeserving," even his daughter Eliza (of the same metal as her dad, of course) is absolutely disgusted.
You see, Eliza is, in fact, trying to better herself.
Alfred Doolittle considers himself as one of the "undeserving poor." Why? Because he does not do any work, doesn't want to do any work, and never plans to do any work, no matter what. Oh, there's a wonderful song in My Fair Lady (the musical version of Pygmalion) that deals in this very issue: "With A Little Bit of Luck." How's this as the answer to your question:
The Lord above gave man an arm of iron
So he could do his job and never shirk.
The Lord gave man an arm of iron-but
With a little bit of luck, With a little bit of luck,
Someone else'll do the blinkin' work!
Sums Afred up quite nicely, eh? Not sure if Shaw could have said it better himself.
Back to the point, though. Why doesn't Alfred Doolittle want to "better himself"? Simple! Alfred Doolittle is perfectly happy the way he is living and has no desire to change it. Ah, but that's about to change thanks to Professor Higgins. : )
He doesn't want any responsiblity and prefers to life off of everyone else.