why couldn't they just steer the ship back to pick up?

This is not a Star Wars movie. They feature fictional physics.

In our reality, ships in space, CAN'T just turn around. They don't have the fuel or supplies to do that.

What you saw in this movie was completely realistic and accurate.

They used the gravitational pull of the Earth, to alter their course, and they received more food in that resupply module.

I don't think it's a stupid question. In space, there is very little resistance. Just point, accelerate briefly (burn) and glide.

Or you can do a very slow long burn, picking up massive speed, using very little fuel. It takes no fuel to maintain your speed.

To turn around, you'd have to do a heavy burn through and beyond the entire turn, and you'd likely run out of fuel before you completed the turn.

They need to slow down the ship and then they need thrust to accelerate it back after turning. They don't have that. That's why they need a gravity assist by slingshotting around the earth in order to not just maintain their velocity but increase it. They also need fuel calculations on whether or not there's enough fuel for this maneuver to get there and back again. To stop a ship requires thrusters in the opposite direction. Then you need thrusters to accelerate again. All of these things require fuel, and mission wasn't designed for these contingencies. That's why NASA wanted the crew back home and to leave Mark to Hermes IV.

A move to go back and rescue him requires a plan. The crew on board cannot just decide to go back, they need authorization from Houston. And if they decide to go rogue they would need the guidance of Houston still, and Houston would never give them orders without a viable plan that's been vetted and the math checked out. The reason they were able to mutiny later is because a viable rescue plan was leaked to them that was checked out by the experts first.

What you're suggesting is to get the Hermes crew to mutiny and go back for him themselves without a carefully laid out plan. They'd have to figure out the plan themselves, and that is not their area of expertise. They were trained to carry out the missions, not to design them.

As stated before in a subthread, a spaceship does not need fuel to continue its flight. Without any friction a spaceship like a planet simply continue its flight only influenced gy gravity which could be complicated for example in swing by maneuvres (used for the Hermes to return to Mars. I didn't read the book but assume that the swing by around the Earth is used for accelerating the ship to shorten the transit).
More important and not mentioned in the answers before:
No real spaceship ever had the fuel to stop. Current example is the New Horizon which flew by the Pluto instead of stopping there. The most important example of slowing down was the Apollo. You can imagine the "payload" as the Lunar Landing module and the cap of the Apollo spaceship containing the astronauts. The rest of the Apollo ship was used to slow down into a Moon orbit (not stopping!) and reaccelerate to an "escape" speed. The Apollo missions did not need to escape Earth or Moon orbit (technically only an orbit reaching the Lagrange point where the Gravity of Earth and Moon cancel out was neccessary), which the Hermes need for reaching Mars. Now imagine the Saturn 5 size in comparison to the Apollo Space ship + Landing Module.
And now the point: To stop a space ship, you do not need only double the fuel, but you have to accelerate the fuel to stop, too. Given the same Energy to stop a ship than to accelerate it, the Rocket to launch the ship incl. break fuel has to have the same relation of weight to its payload (incl. the "stop fuel") than the original ship to its payload. To "return" you need the same relation. To reconstruct a Saturn5 to be able to stop and return, and given the weight by lets say 20:1 rocket to payload you need a rocket 20x20 = 400 times larger than the actual Saturn 5. While for a Hermes spaceship constucted in Earth orbit the exact rules differ, it remains not possible to construct such a ship with chemical or ion thrust.
In reality the "break" to return to Earth surface is using the drag of the athmosphere which is a very brutal and hot method making every manned space flight a deadly risk.
Best regards

Dietmar