I heard this song when I was little. The lyrics are something as follows (vaguely):
"When I was a little boy, my father asked me, what do I want to be? Do I want to be a doctor...". (cannot remember of rest)
This song is more of a nursery rhyme. Given that I am over 25 years old, it is not from My Chemical Romance (as suggested by Google search) without a doubt. I am also certain that this is not a song made up by my parents since I vividly remember hearing it from the radio.
I also tried various song recognization software, but interestingly, still no luck.
Edit: Maybe is it a song from The Carpenters? My mom is a huge fan of their music.