A naysayer is a person who always says "No." Naysayers are negative and cynical — they aren't much fun to be around.
If you respond to every invitation with, "No thanks — I wouldn't have fun anyway," and answer questions about how your day was with a list of complaints, you're a naysayer. It's your negative, pessimistic attitude that makes you a naysayer. In the 1600s a nay-say was a "refusal," from the now less common use of nay to mean "no."