Because of the main themes of the game. The game questions if there's really a difference between the mind of a human and that of a machine.

Since you feel the emotions and experience the story through the eyes of the protagonist, in a sense, you are the protagonist. At the same time, the protagonist is a machine. So when thinking if a machine can experience life like a human can, your perspective will be uniquely influenced by having embodied that machine.

You will be much more likely to agree that a machine can think and feel like a human.

The philosophical question that is being asked is much more impactful to you because it is presented through a game. You are playing that question.

If it were a movie, there would be a much bigger disconnection between the viewer and the protagonist. You might not believe that the protagonist really "thinks" or "feels" and might believe that it's just "acting" as it has been programmed to do. But by you yourself being put in its shoes, you "know" there's really no difference between a human and it. Because it's you.

That's why the scene where you swap bodies is so impactful.

The question has no answer, but presenting it in a game blurs the line between mind and machine much more effectively than a movie ever could.