During the intro to Singin' in the Rain, Hollywood star Don Lockwood shows up at the launch party for his latest movie. The venue is packed with adoring fans, and Don gives a brief speech about how he got to where he is today, how his well-off parents got him into the best schools, he studied the classics, had the best theatrical training money could buy, and so on.
But while he's talking, the movie is showing his actual background, growing up as a poor kid, dancing in run-down pool halls for tips, sneaking into movies because he didn't have two nickels to rub together, performing in tacky Vaudeville acts before he got his "lucky break" in show business as a stunt man, being on the receiving end of all sorts of abuse from the stunts, until he just happened to impress the producer who decided to give him his first leading role, and the rest was history.
Lockwood is portrayed in the film as a man of considerable eloquence and charisma, and his true story, if he had put real effort into telling it well, could have made quite the compelling underdog tale. The audience would have eaten it up. So why lie about it and make up a much less interesting past for himself?
Obviously the out-of-universe reason is for the audience to be amused by the dissonance between what Lockwood is saying and what the camera is showing to be true, but what's the in-universe reason?