Why would the government hide the fact that the Earth is round from us?
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Not a Flat Earther, but read the wiki first.
I have read the wiki on this question, because that is what fascinates me the most about the FE belief. You have to be convinced that an incredibly elaborate complex of lies is actively maintained. Not just NASA, but the whole field of astronomy, for starters, has to be a lie.
And why would some sort of nefarious conspiracy come up with such an incredible web of lies? What could be their motivation to write libraries full of elaborate lies about a fantasy universe, when the topic only interests a small minority of people to begin with? What could they gain from it?
It fascinates me how anyone can seriously believe this. So yes, I did read the wiki. Does it answer the question? No, not really. The wiki says, under conspiracy/motivation:
The purpose of NASA is to fake the concept of space travel to further America's militaristic dominance of space. Some other superpowers are supposedly involved as well: pretending and/or lying about a space program in order to scare other countries.
This could maybe be an explanation for a fake NASA. But if their only goal is to scare other countries, how does it help to lie about the shape of the earth? How does it help to come up with libraries full of internally consistent fake info about a universe, including black holes, galaxies, competing theories about dark matter, all supported by incredibly advanced math, all of these pictures you would have to fake...
And then they would also have to fake every map of the earth, every travel path of every vehicle making a long journey.. and they would need to get so many peoples to cooperate with their scheme... none of which really helps with military dominance.
So no, the wiki doesn't answer the question.