In the intro cinematic Walker tells Church the ins and outs of the Antaeus. He also mentions that the vessel was designed so that the captain has to be a physical person, unlike the people only existing in digital forms on Soulcatcher chips. Just as Walker starts to explain more about this, their superior interrupts.

So, the writing sets up the nature of the Captain as a mystery, but it never reveals anything more about it. What is the deal here? Did the Captain go down with the ship and somehow remain preserved for the twenty years the Antaeus was at the bottom of the ocean? What exactly is this person? Is it a person? I'm guessing the Captain isn't just some veteran who lived peacefully for the last twenty years, since it wouldn't be such a big deal if it was something so simple.

Aren't you (the player) the captain? Seems to make the most sense to me.

Good question. I don't think the developers thought that much into it. They may have designed it that way to make it seem more ambiguous and flatter the player by making them feel in control of the situation lmao although that's just me...

There was a lot of discussion about it at the time the game was released. In essence, the captain is the entire brain/nervous system of a human being, implanted into the carrier's command system. Soulcatchers wouldn't work in a carrier, because(a normal soulcatcher can act somewhat autonomously, but it can't make decision etc. It's just a soldier. That was insufficient for the Antaeus captains, so they stored an entire human being, cerebrally, into the carrier.

There's a hint given in the intro, where it says that carrier 4 suffered cerebral damage and isn't responding to commands. Ie, the captain is braindead.