fuddy-duddy
A person who is old-fashioned and dislikes new or fun things.
A fuddy-duddy is someone, usually older, who seems old-fashioned, fussy, and resistant to new ideas or fun. If your grandmother complains that your music is just noise and insists that nothing good has been written since 1965, she's being a bit of a fuddy-duddy. If a teacher refuses to let students work together because “we never did that in my day,” that teacher is acting like a fuddy-duddy.
The term suggests someone who's overly proper, set in their ways, and uncomfortable with change or anything too lively. A fuddy-duddy might object to harmless fun, insist on outdated rules, or dismiss anything modern as foolish. Picture someone tutting disapprovingly at kids playing loudly in the park or refusing to try a smartphone because “those contraptions are unnecessary.”
The phrase has a silly, bouncing sound to it, which matches its slightly mocking but not mean-spirited tone. When you call someone a fuddy-duddy, you're gently teasing them for being stuck in the past. Interestingly, young people can act like fuddy-duddies too: that classmate who insists the old way of doing a group project is the only right way, even when better methods exist.