There’s not a great deal of mystery as to the speaker in this song. It’s Billy Joel. The song begins with events of 1949, the year he was born, and it ends with events of 1989, the year he turned 40, an event which prompted Joel to look back on his life. “I had turned forty. It was 1989 and I said ‘Okay, what's happened in my life?’"
But it might be added that the speaker is Billy Joel with a bit of a chip on his shoulder. He was inspired to write the song by comments made by a younger person about the impact that Joel’s generation had had on the world. What he hoped to convey was that “we didn’t start this stuff, we inherited it” (Rolling Stone, 16 November 1989).
Based on this explanation, the speaker might be more broadly identified as Joel’s entire generation—the Baby Boomers. This label is applied to persons born right after World War II—or more precisely, between 1945 and 1964. With Joel speaking on their behalf, the message would be that most of the problems plaguing the world between 1949 and 1989—the Cold War, turmoil in the Middle East, racial discrimination, Edsels—were the fault of their parents. In other words, the criticism aimed at Joel’s generation should be kicked upstairs a rung or two to the people that came before. We here at Shmoop get it; we blame our parents for all of our mistakes, too. Why didn’t Daddy Shmoop love us? Why? WHY?!?