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: 
The mining companies are being subsidized
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Drones would have been better value for money, but the government subsidizes human labor.
This is done to keep the population (especially the men) occupied and also safely locked away, not giving them a chance to sit around talking rebellion.

This is also the reason space mining is not favored: there are too many places to run and hide once the tech for space colonization exists.
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 ;-)