Drying happens when the moisture on your dishes gets evaporated into the air. If the air is already moist. It happens slowly. The air in the just opened dishwasher is hot and very moist. Blowing away removes the vapour/ moist air from the washer compartment, which gets replaced by the drier air in the kitchen. Blowing towards just keeps the moisture circulating inside, and though some of it will no doubt eddy out, it isn't as efficient, it seems.

Maybe something to do with vapor pressure?

How close is the fan to the dishes? Moving it away and pointing it towards them may work better than being close and blowing.

Everyone needs vacuum cleaners, nobody needs leafblowers.

When you're sucking the air away it still generates a current over the dishes, but also carries the saturated moist air away so that new drier air replaces it, which becomes saturated and carries more moisture away. When you're blowing the moving air impacts upon the dishes and breaks the flow so the moisture stays closer to the dishes.

Just guessing though.

Blowing into an enclosed space is chaotic, the fan has to push against air currents being deflected. Blowing into an open space (aka sucking out of you dishwasher) is much more orderly, the fan can simply pull the air out and there are much fewer air currents running orthogonal.

This is as far as my very basic knowledge goes here. You can try this effect by exhaling and inhaling air through a barely open mouth or a straw.

EDIT: On a related note, never "blow" during fellatio.

because blowing sucks.

Isn't this just a simple case of "get the moisture away"? Blowing into the dishwasher doesn't move the moist air away, it just moves it around in the box. Blowing out pulls the moist air away from the dishes and out into the room.

If your box fan was pushing dry hot air (like a hair dryer), hot enough to meaningfully speed up evaporation, then blowing in would probably be better.

So you're saying that blowing sucks, and sucking blows?

...okay, serious now. I think that it has to do with air pressure - sucking reduces it while blowing increases it. And water evaporation happens faster on regions with lower pressure.

Blowing air into a confined space doesn't really work well. It's the same reason why pointing a fan into a hot room doesn't cool it down any; the air needs somewhere to flow to, and it can't go out the way it came in because there's a fan pushing it back. So the air in the room might move around a bit, but it isn't circulating hardly any of the air from the rest of your house, which is why that room stays warm even though you "feel" the wind from the fan. But if you open some windows in the house and do the same thing, you now have place for the air to move to, so it doesn't just spin around the same container any longer.

Sucking pulls the air in from all directions, whereas on the other side of the fan it’s being blown out in a stream.

Why is sucking better than blowing?

Ummm... not a girl, but I suspect it's easier to suck things out of it than blow into it...

I would guess that it's moving moisture away from the vicinity. Blowing it far away instead of inwards to the kitchen. Then normal evaporation can happen better.

But I think you really don't need to bother, why not just let them dry?

Maybe it is something similar or related to: https://youtu.be/XP6oqIic4lo (apologies for youtube link)

While blowing, some of the fan's energy is spent on increasing the pressure inside your dishwasher, which increases the density of the air the fan blades move through, increasing drag on the fan blades causing them to move slower and create less airflow.

While blowing, you're also pushing moist air to the back of the dishwasher, and after that air reaches 100% relative humidity, it can't hold any more water and will not help dry your plates. Some of it will eventually escape around the sides, but some of the airflow your fan creates just circulates humid air around the inside of the dishwasher.

Turning your fan around solved both problems. It increased the volume of air flow, and decreased the relative humidity of the air flow.