It's very tough to explain to someone who hasn't worked on large multidisciplinary projects with mandates to push some sort of boundaries like in exploration, science, and technology. This isn't some theoretical discussion by futurists, there is ample evidence that these kinds of ventures have systemic effects that touch literally every person, socioeconomic class, and daily activity. Academia and private industry have pathological problems with compartmentalization that have a real impact on the exchange of ideas and progress - entire companies like Toyota have risen to the "top of the world" based solely on their ability to open up communication between line workers, robotics engineers, and designers under a common vision. To Toyota that vision is their emphasis on quality control, for NASA and Apollo it was the mandate to beat the Soviet Union to space and to the Moon. Just the act of bringing so many different engineering, scientists, and other people together to work on a single problem like going to the moon allows them to tackle issues that were intractable to each of them individually. Many problems, especially as technology develops, require a solution that is novel across several different fields.
These mandates are powerful. The mandate to defend the nation led to radar and telecommunications, transistors, and many other technologies in use by almost everyone. The mandate to make it to the moon led to a revolution in material science that is now part of every car and phone, it allowed us to map the world and put it in half the world's pocket, and even created a whole new field, systems engineering, that is dedicated to the science of managing gigantic projects spanning thousands of engineers, scientists, manufacturers, and so on. The Human Genome Project, another massive multibillion dollar venture unlocked the human genome to the world for the first time and is directly responsible for much of the biotech boom in the last few decades.
As for "many people don't know that we went to the moon", I'm not so sure that's actually true. Carl Sagan wrote in the Pale Blue Dot in the 90s:
A scientific colleague tells me about a recent trip to the New Guinea highlands where she visited a stone age culture hardly contacted by Western civilization. They were ignorant of wristwatches, soft drinks, and frozen food. But they knew about Apollo 11. They knew that humans had walked on the Moon. They knew the names of Armstrong and Aldrin and Collins. They wanted to know who was visiting the Moon these days.
You're underestimating the biological human desire for exploration - it is a basic evolutionary survival mechanism.