Question: In the near future the demand for resources only rises due to both a ever growing population, energy and resource crises, and rampant consumerism. Peak oil has been reached, scarce resources like platinum, silver, and other rare metals have been depleted on the surface, and the world is beginning to feel the more drastic effects of climate change such as mass extinctions of animals and strains of crops. In this rather bleak period the major mining companies looked to the seas to solve the mineral requirements of earth. While mining the seas isn't a easy affair the ocean's mineral wealth is virtually untapped.

However instead of using drones to mine both ores and the methane ice the big companies used mainly human labor (with drone assistance), but why? What benefit would human laborers in deep sea rigs have over a aquatic drone?

Note:

The population is fed mainly by cultured meat and indoor+vertical farming hence why the population is expanding even though the climate looks bleak.

Asteroid mining isn't considered a good alternative for earth due to the transportation of the goods back to earth. However if necessary the industry does exist (mainly for the initial space colonies)

The mines would be accessed by either mining ships or for the larger mines maglev trains connected to large underwater bases (with the tunnels dug under the ocean's surface)

Answer: 
In dangerous places (like outer space, deep sea etc) the only reason to use people instead robots is that in general **people are more flexible and much universal than** single **robot**.

But it's only one side.
Human flexibility reduces in deep sea because of great pressure. Withstand to such pressure much harder that operating in outer space. People should use heavy 'deep' suits even in not-really-deep sea. Even in such deep human couldn't operate by hand but only by specialized instrument **integrated with suite**. But.. you could give this instrument to a robot and direct it remotely! (Robots don't need air and food and it's not a problem to lost some)

Here we could say that remote manipulation requires some reliable communication, calculate costs and go deeper in rabbit hole. But it's out of scope.

So if you really want to get people mining in deep sea *in your world*, you have to **introduce intermediate bases where people would live and operate** nearby drones and do something special which is unreasonable to do on surface. [Repairing drones is an example] 
So your question could be reduced to another one: **What benefits to use intermediate inhabited bases?**  

Some reasons have been already described (communication and repairing on-site is cheaper). If you look at space programs like ISS or lunar base you probably could add more like 

* New technologies
* Proof of national superiority
* Communication with intelligent ~~aliens~~ deep-sea creatures
* Universe exploring and understanding
* Factories which produce not a raw resource but goods with high added value [like engines instead of raw steel]. And those factories couldn't be employed without human *in your world*. [Because in near future it (probably) will be possible in our world]

or invent something own. Or ask new question on this site ;-)
I agree with much of what Shadowzee has to say about profitability. Modern corporations operate with one thing in mind. Increasing profits for shareholders. Human labor can be VERY inexpensive. It can be the largest cost a business might incur. However there was something Shadowzee didn't mention I don't think. If you look at history governments and business have had little concern with the civil rights of human labor. There are numerous examples. Improved quality of life for working class people is only a fairly recent development. And quite frankly increases in inequality in this country suggest to me that that particular trend has the potential to reverse itself.

What kind of future are you envisioning? A good one...A dark one? If you can think of a scenario which involves coerced unskilled labor you might be able to come up with something along the lines of what I am thinking i.e. some corporate entity viewing the trade-off between expendable low cost unskilled labor and expensive automation that requires AI and coming up with a "unique and inexpensive compromise" - automated human beings with implanted programmable chips to perform the labor of the machines.

There are many people who see the combination of human and machine as a natural part of human evolution (e.g Elon Musk, Ray Kurweil). Corporations might see this as highly beneficial approach to both labor problems, automation problems and what happens if you don't have wage slaves earning money to buy the stuff they sell. 

Can't speak to mining the deep sea because I would think this is pretty difficult work and would probably require highly skilled labor rather than unskilled labor. But what about programmable chips to increase the laborer's skill set. 

I could see a future where you could have a labor pool that just needs to eat and might 
allow themselves to subjected to it. Or forced labor from criminal and political dissident populations. 

Sorry...that is a pretty dark scenario but mining industries don't treat their workers very well as a general rule.