When you intellectualize something, you think and talk about it with your head, not with your feelings. You use serious, careful, rather complicated words. You might say “this is a problem of trust” instead of “I feel hurt.” People often do this when feelings are hard: the mind stays busy so the heart does not have to speak. Teachers who study the mind use this word for that habit. It can sound a little cold, a little critical — as if you are hiding behind ideas. American English writes intellectualize; British English often writes intellectualise. It does not mean “to make someone clever.”