#Btw I think another reason why Minkowski cuts Eiffel off in this scene is because

[hephaestuscrew]

If you want to add another emotional layer to these thoughts, you can think about the way Minkowski tells Eiffel "Listen to - [...] LISTEN TO ME!" in their conversation before the Sol blasts off. She speaks over him and cuts off his protests to ask him to listen. She's desperate to explain herself to him. She really wants him to understand her reasons for sending him back. But even so, she doesn't explicitly tell him what I'd argue is the most significant reason for her action (her care for Eiffel as an individual). I think there's a kind of tension there - the intense desire for her motivations to be understood, versus an unsurmounted difficulty in directly expressing all of those motivations.

I'm always emotional about the fact that, when Minkowski tries to justify her choice to send Eiffel back to Earth on the Sol in the finale, she never directly expresses a reason for her decision that's specific to him. 

She tells Hera, Lovelace and Jacobi "If - if - we don't make it through this... if we don't stop this... people need to know what's coming. They need to know what's happened." She gives them a reason which is logical, practical, and impersonal. It's a 'big picture' reason, focused on humanity as a whole. Minkowski's own emotions don't really enter into this justification at all. That's the kind of decision-making she wants her crew to think she's using. If this was Minkowski's main motivation, it wouldn't matter who was sent back, so long as they could explain Cutter and Pryce's plan. I don't think Hera, Lovelace, or Jacobi believe that this was the main reason why Minkowski sent Eiffel back, and I'm not sure whether Minkowski expected to actually convince them. 

Jacobi asks "did you tell him that before or after you sent him on his merry?" But in fact, Minkowski didn't tell Eiffel at any point that he needed to tell the world about events on the Hephaestus. If her primary motivation had been about having someone to deliver a message back to Earth, she would have given Eiffel suitable instructions - she wouldn't have just trusted him to figure it out. 

Instead, the most direct reason she gives to Eiffel himself for why she's sending him back to Earth is "I need to know that at least one of us makes it back. That I got someone through this." This is a more personal reason, where Minkowski's emotions are relevant, but it's still not explicitly about Eiffel himself. It's about saving "at least one of us", as if it doesn't matter who that "somebody" is. I think this justification is closer to the core of Minkowski's motivations than what she tells the others afterwards. Her responsibilities to her crew as a Commander have always been important to her, and she doesn't want to have failed in keeping them safe. And Eiffel is the only member of her original crew who she's able to save in this way. Hilbert is dead, and transferring Hera over to the Sol to be sent back to Earth on her own would come with a whole host of problems. 

But I don't believe for a moment that the reasons she sends Eiffel back are purely practical and abstract. I don't believe for a moment there's no personal significance to her decision to save him specifically. I don't believe for a moment that it was all about her practical plan for the wellbeing of humanity, or her desire to have fulfilled her duty to at least one non-specific member of her crew. She doesn't just need to save "someone". She doesn't just need to save "at least one of us". She needs to save Eiffel. She needs to save her friend.

The closest she gets to saying aloud that her motivation is about her care for Eiffel in particular is when she says "Go home, Eiffel. Hug your daughter. [...] Goodbye, Doug." She was prepared for those to be the last words she might ever say to him. And there's at least something in these lines that implies she wants Eiffel specifically to return to Earth. I don't think it's that she saves him because he has a daughter. I think when she tells him to go home and hug his daughter, it represents more than that. It's about how she wants him to be able to move forward and live his life. It's her saying that he deserves the interpersonal connections that are valuable to him. It's about her not wanting his story to end there on the Hephaestus. 

It kind of breaks my heart that even in that situation, she can't fully say aloud that the reason she wants Eiffel to survive is because she cares about him specifically. She has to give the justifications that are about her as a Commander and not about Eiffel as her friend. She doesn't tell him that she's saving him for his own sake, because he matters to her so deeply, because his safety is so important to her. 

And I really wish I could believe that Eiffel didn't need her to say it, that he could just understand just from her actions how much she cares about him. But as the Sol flies away from the Hephaestus, he tells himself that he's there because he "never had quite as much chest hair as Lieutenant Commander Renée [Minkowski]" and because he "could never get it right". So I don't think Eiffel ever really appreciates that Minkowski sends him back not because of what he can't do, but because of who he is: her friend, one of the most important people to her, someone who has brought so much value to her life, and someone whose death she refuses to contemplate.