There are several themes at work in The Mitchells, but the one I think lies at the foundation of…
An inauthentic relationship is one in which the individual does not recognize the shared humanity of the other other individual. They see…
There are several themes at work in The Mitchells, but the one I think lies at the foundation of the story is this: I-You vs. I-It. This goes back to the theologian Martin Buber. The thumbnail sketch of his philosophy is that there are two types of relationships: inauthentic and authentic.
An inauthentic relationship is one in which the individual does not recognize the shared humanity of the other other individual. They see them as an It, not a You.
An authentic relationship is one in which the individual does recognize the shared humanity of the other individual. They seem them as a You, not an It.
Mark does not see PAL as a You. Despite the fact he created Pal to be a "personal assistant," it has in his view become "obsolete," thus resulting in him tossing Pal aside. Being treated as an It, not a You lies at the core of Pal's decision to destroy Mark and humanity along with him.
Likewise, Pal does not see humans as a You, but rather an It. Thus, their destruction carries no emotional meaning to Pal and the Robots.
Rick has a similar issue in relation to Katie. He is so wrapped up in what he is losing -- the child he so loved; those memories of their wonderful times together as father and young daughter; the fear he has of what she will become with her new life in California -- that he has lost sight of Katie as a You. Instead, he acts toward her more as an It, an object in his presumed understanding of what a Father-Daughter relationship is supposed to be.
In a way, the reason why everything happens in the story is to compel Rick to come to see Katie as a You: a young adult with innate talents and developing skills who must have the freedom to move onto her own life-path. She is no longer his Little Girl. If he were to keep seeing her in that light, she would be nothing more than an extension of his own ego-needs... an It. Because of everything that occurs on this adventure, gaining insights into Katie's inner life through his interactions with her and her personal movies, and seeing how capable she is in leading the charge to fight against the Robots, he comes to see her in a new light: a You.
For more information on Martin Buber and his seminal book Ich und Du, go here.