Between the end of the last episode and the beginning of this one, the Doctor apparently told Courtney she wasn't special, which has led to her going off the rails at school. Clara and the Doctor find her in the TARDIS -- now sporting motion sickness bracelets so she's ready for another trip -- where Courtney confronts him about whether he really thinks she isn't special. (And does the TARDIS not have door locks anymore?) This is the point at which any of the other modern Doctors would launch into a speech about how everyone is special, but instead the Doctor decides he can make her special by taking her to the moon in 2049, where she'll be the first woman to walk on its surface.
Though Courtney seems trilled by the idea, it's an awfully manipulative move by the Doctor -- and this kind of cold-hearted manipulation continues throughout the episode. When they land inside a space shuttle headed to the moon and are confronted by the ship's astronauts, the Doctor tells them to "shoot the little girl first," prompting Courtney to hide behind Clara, where she sits on the floor and rocks back and forth.
Ouch. Capaldi's version of the Doctor isn't the friendly alien we've come to know through the portrayals of David Tennant and Matt Smith, and while I think this grouchy version of the Doctor could certainly work -- not unlike Christopher Eccleston's outwardly gruff portrayal -- at this point we've had a lot of episodes of him being a jerk to everyone with few signs that he cares about anyone or anything, which makes him hard to sympathize with. And in this episode, he's really at his worst.
It turns out that the three astronauts have come to the moon in a 1980s era space shuttle packed with nuclear bombs because the moon has been increasing in mass, which has caused the tides on earth to go haywire -- the biggest natural disaster in human history -- which they apparently plan to fix by blowing it up. (Get it? They're going to Kill the Moon.) This is basically Doctor Who's version of Armageddon except Armageddon was probably more scientifically sound.
So why would you go to the moon in 2049 in a 1980s space shuttle -- especially considering that the shuttles are currently on display in museums and stripped of working parts? Lundvik, the leader of the astronauts, explains that no one cares about going to space anymore. Though it's certainly a nod to the defunding of space programs, it's a tremendously pessimistic view of the future... and it's also belied by present day fact. Even with reduced funding, NASA plans to have a new space vehicle that's capable of sending manned missions to Mars by 2030. China, Europe, India, Japan, and Russia all have space programs that are actively working to explore our solar system -- and many more countries have space programs and even send astronauts to the International Space Station. And that's not even considering private companies like SpaceX, which is currently making some of the biggest strides in the industry.
Are we really saying that between 2014 and 2049 not only will none of those programs have made any progress but they won't even exist anymore? Lundvik comments that the shuttle is second-hand, a repaired museum piece, and the astronauts are "third-hand" by way of explaining their lack of expertise. This is an exceptionally bleak view of the future and difficult to believe it... which makes it hard to follow through on the rest of the premise, which only gets weirder.