Worried about whatsapp and spying

I know that this question has been answered many times before but does someone know if whatsapp can be spyed or seen by other people? An acquitance of mine ensured me recently that it's completely possible and showed me messages from a conversation alien to him.
I thought it a lie at beginning, but he started teasing me by throwing little references to chats that I had with my friends and boyfriend via whatsapp, and of course it is starting to worry me. I know about monitor software and that he needs the phone to install it, he may have had access to mine at some point, but I'm almost sure that he didn't have access to the first person's phone...
Is he just toying me out or not? How can I see if I have any monitor software installed or how does he know so much??
Would really appreciate any light in this...