His parents may be very traditional... and he is uncertain about their reaction.
It means he is a gutless turd.
It means that when he finally does tell them, they will probably not accept you or the child. At least that is how it was when my daughter's fiance wouldn't tell his parents about her son. They went ahead and got married anyhow. It lasted 5 years before his parents finally made her and her boy so miserable they finally left. And he let them go, because he was his parents little boy, never did become a man. After the divorce, he married the girl his parents had picked out for him.