Imagine you are crew, standing on a ship. You are facing east, and the bow of the ship is facing north. It’s night and there is a thick fog.

You hear a cry “man overboard on the left!”

Where is the overboard person? Are they to your left, the ships left, or the left of the person shouting?

If the cry is instead “man overboard on the port side!” there is no question.

Great points. And I'd add that thanks to wind and water, ships can also move in directions besides the obvious one. So it's possible in this case the boat could be moving west, giving another direction that left could be relative to.

This feels contrived, to be honest. Late at night on a vehicle that isn't moving with no other discerning factors to distinguish things, and you are basically screwed. Though, realistically, you are just going to wherever the shouting is coming from, you are not going to go slow to orient yourself to the vehicle. Even better, someone would yell something even more defining for where to catch someone that is going to be specific to the boat you are on. (Well, more realistically, you have hopefully practiced emergency drills such that the term is almost irrelevant, you have practiced so much.)

This is about as worrisome as "you are the fire department, and you are told you need to rescue some people on the 14th floor. Quick, does that mean you go up 13 flights of stairs, or 11?" Realistically, you aren't getting it right on spur of the moment decision making.

Any room for error is a guarantee that a human will mess it up. Left already has a definition, so there's room for confusion; a word specifically talking about the ship is more concise.

Whether "the left" means your left, the ship's left or yet another left (the harbour's?) is highly ambiguous. You can't assume that everyone will instantly understand this correctly.

I think starboard and port make more sense here because they only describe parts of the ship, so the meaning of the terms is completely unambiguous.

"Left" vs "the left" is not good enough. That could still mean either concept semantically, and you can't be sure the person speaking to you didn't mess up the convention when the two are that close.

A crew (any kind of crew) requires exceedingly clear communication. "Ship left" and "ship right" could work, but what if the environment is noisy and you're not sure if the first word was "ship" or something else? Domain-specific, unique terms are fantastic tools for crews.

Pass that to the left

As opposed to "the other left".

There are other uses for the definite article. E.g., "Down the hall and on the left." It's also used in relation to motion. "Go to the left of that ship." Even if you went with it, though, it still has the potential to be confusing.

Speaking as somebody who sails occasionally, to me "left" and "port" are just very different concepts. It's sort of like driver's side and passenger's side of the car, but more intense. So I think the desire to use "left" mainly comes from people who don't spend much time on ships, an audience, not particularly important to sailors. Sort of like how non-programmers might struggle with some of our technical terms, but we'd never change.