Electrical – Old wiring in house has cable with 2 white wires and one black. Trying to install new ceiling fan

From an edit, of all things:

The wiring was as the commenters suggested (one switch going to the light/fan and one switch for an outlet in the room). I hired an electrician to come change it so one switch works the fan and one works the light on the fan.

That's not really a white wire coming out of your fan control

When the instructions for your fan control say a wire is "black/white" -- they mean it's a black wire with white stripes on it, which has nothing to do with the white neutral wires in your box.

As to wiring up the fan control...

The new fan control gets wired as follows, then:

• Green gets nutted in with the rest of the greens
• Black/white gets nutted to the bundle of red wires that the two bottom black wires came off of (the two bottom black pigtails can be removed and saved for use down the road)
• Black gets nutted to the black that was nutted to the top right black pigtail
• And blue gets nutted to the red that was nutted to the top left black pigtail

You'll also need a two-gang faceplate that has a decorator opening on one side and a blank space on the other -- either that, or a decorator opening blank for your existing faceplate, considering that the new control only takes up a single gang of box space.

And to the fan itself

The fan, though, is a bit easier to wire:

• Ceiling red to fan blue
• Ceiling black to fan black
• Ceiling white to fan orange and white
• Ceiling green bundle to fan green

As to mounting that fan...

Your box is likely a special type of box known as a concrete box that was poured right into the ceiling. This type of box, however, does not have the correct setup for mounting a fan to it (the mounting ears will bend if you try, letting the fan fall on your head). So, you'll need to use masonry fasteners to mount the fan to the concrete surrounding the box, instead.