For reference, I have already told them why the sky has no stars (it's because of camera exposure, the moon surface is very reflective so lower exposure is used to not overexpose the image) and why the flag wasn't drooping down (there was an extending arm in the stand to hold it upright, as a flag drooping down is a sad flag). I have also explained that the videos of the moon landing were upscaled/remastered when they asked why the video quality of the clips were so good.
Currently, their main argument is the fact that the U.S. were able to do the moon landing in the mid 20th century while are experiencing delays for the current moon mission. They argue that, if the moon landing could be done way back then, with modern technology, it should be possible to quickly get back to the moon. They also argue NASA could have just reused the same designs as the Apollo missions if they actually went to the moon.
I have argued that NASA's budget is a fraction of what is used to be, and that the addition of new modern technologies introduces additional parts that could break and thus need to be tested. I have also mentioned that the Soviet Union would immediately call out the US if they faked the moon landing, and that samples of moon rocks were sent to Soviet scientists to study and verify. They insist that the Soviets were scared of what the US would do if they spoke out against a fake moon landing, which I didn't agree with (given they were both nuclear superpowers)
They then argued that it's impossible to tell whether the moon rocks are actually from the moon landing, they could be samples collected by rovers. I responded that no rovers had successfully collected moon rocks at the time, and then they switched to arguing that it's impossible to verify the rocks are from the moon. I followed up by saying there are methods of doing that (through the composition of the rocks and such). They then asked how anybody knows what moon rocks look like if nobody else has been to the moon, and I got kind of stumped. I tried to explain that there are models to how the moon formed, how we know the rocks aren't from Earth, satellites that map out the surface, etc., but they reiterated that no one can "prove" that they were from the moon without going there in the first place.
One interesting thing they also mentioned is that, if the US really did do a moon landing, why the Soviets (during cold war era) or Chinese (in modern era) didn't do what they do best and copied their designs to land on the moon. Given that the US and China are having a new space race with the goal of being the first to establish a lunar base, they argue that China could just copy the Apollo program designs if the US really did do a moon landing.
To summarise, their main points/questions right now are: a) Explain why the US hasn't gone back in so long, and why with modern technology it seems so difficult? (especially given that NASA has been experiencing numerous delays in the Artemis missions, that certainly hasn't given them a good impression...) b) How do you verify moon rocks without having actually been on the moon? How did scientists figure out what a moon rock looks like? c) Why aren't the old Apollo designs being reused for a moon landing? (by either the Americans or the Chinese)
They say that there isn't strong evidence either side (but believes that it is false, saying that "we will see" once someone else lands on the moon)
And what other points can I bring up to definitively say, yes, the moon landing wasn't faked?
edit:
Another thing, they also can't believe that astronauts could bring and ride the little moon buggies. I am also partially interested in how that was achieved to be honest!