As for the trolley dilemma, it's a great thought experiment precisely because people's answers and their reasons for their answers differ. I'm not sure therefore of its relevance here. Presumably the person you're responding to can just be consistent in their response to both the question about airports and the trolley dilemma.
Of course if that's genuinely the situation, it's hard to argue that the needs of the many shouldn't be paramount. But in the case of airport expansion, it's rarely that simple!
A bigger airport isn't necessarily a public good. If it's close to urban areas it's often a net detriment to the public good, inflicting more noise and pollution on millions of people. The drive to expand really comes from the airport operator's desire to increase flight numbers and profits.
So how many people should be able to block an airport extension? a hundred people, ten thousand people?
What you're arguing is the classic of the trolley dilemma [1], the individual vs the many. Should you harm 1 person to save 1 million. The difference here is that you're not killing the individual, you're demolishing their home, and you're not saving 1 million people, you're making travel a little more convenient.
[1] https://theconversation.com/the-trolley-dilemma-would-you-ki...