It's very hard because they see "big data" as something that important people and important companies do. When you say "We don't have big data!", it translates to "We aren't that important!" This, of course, makes everyone very angry.

Be mindful of people looking to introduce big data without justification. They are playing a game of some sort (maybe just personal resume value, or maybe a larger vie for power), and you are positioning yourself as their opponent when you try to stop the proposal they're pushing. Do not go into this naively.