Just explain how you feel. Another common reason I hear often is that “partner” sounds more serious/committed and can be a good term to use if you’ve been together long enough that boyfriend/girlfriend sounds juvenile and inadequate.
My most recent ex had this conversation with me once - “Can we start referring to each other as ‘partner’?” - and I think his reasons had to do with what I said above about seriousness and commitedness. But keep in mind that you can’t MAKE someone refer to you that way. They can do what they want, but it’s fine for you to express a preference.