Halfling monk uses their move to enter an opponents square, free action to drop prone, action to unbroken air them away...ie up, cuz they are prone, stands up and moves 5' out of the opponents square.

Is this a question or a statement?

neither, it's RAW, read a thing where JC said you can't push 'up' , I disagreed and found a RAW that did. But a DM has final say on anything, so doesn't matter too much. *shrug* just mostly put this out here cuz I see a lot of posts that reference JC's twitter posts, usually he's wrong for RAW, but he's 100% right for a DM. Do with it what you will. ^.^

 I also like that this can 'look' like Guiles Flash Kick. ^.^

Halflings can move through an occupied space, but they can't stop there and take an action

RAW they can.  You can break up your movement on your turn, using some of your speed before and after your action. For example, if you have a speed of 30 feet, you can move 10 feet, take your action, and then move 20 feet. Whether a creature is a friend or an enemy, you can't willingly end your move in its space. Nothing says you can't take an action while in the enemy's square.

Technically that is true RAW. However, being prone does not have any RAW effect whatsoever on the direction of an attack. There is absolutely no RAW justification to say your effect will blast the target upwards. The only description for the direction is "away from you." If you're currently in another creature's space that could potentially be any direction; again, being prone does not mean you are beneath the target as you are still occupying the same space. As there is no specific rule that I am aware of detailing how to determine the direction of a push effect originating in the same space as the target that would make it entirely the DM's call. 

In a game like D&D you can try to "do" literally anything you can imagine and it's impossible to create rules for every single possible situation. Also, the more rules that are created, the more complex and difficult to learn the game begins. If you want an example try looking up grappling rules from earlier editions, there are good reasons that said rules are frequently used as an example of convoluted and difficult to understand rules. In your specific case the DM very well could decide to allow your proposed action but the general response is going to be "that ability was never intended to be used like that, tough cookie." Additionally, being in the same space and prone doesn't even suggest in any way that you're directly under them, presumably between their feet, especially when in combat and while they are presumably in some sort of defensive stance. At best some DMs might grant you knocking the target upwards in a diagonal direction but even that is being generous. Again, the hyper-specific use you are proposing was obviously not what the game designers were thinking of when they made that ability and enforcing common sense (specifically being able to say "No, that's just not going to work like that") is one of a DMs most important jobs. 

In what way is he “usually he's wrong for RAW”?

Considering RAW mean "Rules As Written" and Crawford is one of the people that not only literally writes the rules but also has final official say on them that's a very dubious statement. Also I'm unaware of any RAW that explicitly states you can shove directly up while occupying the same space as your target (closest official thing I can think of is a spell from 3.5 called defenestrating sphere and that's a different edition).  If you were somehow actually below your target that's a different thing, but the OP's situation explicitly depends on sharing a space with the target.

Quote from Ashleigh >>

RAW they can.  You can break up your movement on your turn, using some of your speed before and after your action. For example, if you have a speed of 30 feet, you can move 10 feet, take your action, and then move 20 feet. Whether a creature is a friend or an enemy, you can't willingly end your move in its space. Nothing says you can't take an action while in the enemy's square.

Moving Around Other Creatures

You can move through a nonhostile creature’s space. In contrast, you can move through a hostile creature’s space only if the creature is at least two sizes larger or smaller than you. Remember that another creature’s space is difficult terrain for you.

Whether a creature is a friend or an enemy, you can’t willingly end your move in its space.

You have to stop moving to take an action, and you can't stop in another creature's space.

What, exactly, do you think the word "through" means? If they'd wanted you to be allowed to stop in another creature's space, the feature would have said "into", not "through"

Halfling Nimbleness

You can move through the space of any creature that is of a size larger than yours.

Rules allow Moving Around Other Creature at least two sizes larger or smaller than you, and only one size larger with Halfling Nimbleness but you otherwise still can't willingly end your move in any creature's space.

And even if you could do this, why would that mean you'd be pushing up? 

Being inside their space does not mean you are under them. Their "space" is the space they control in combat, not literally the space their body occupies. A medium human is not actually 5 by 5 feet wide. 

What you describe would essentially moving up close to an enemy, dropping prone, and then punching their feet. Looks more like Birdie's Bull Slider.

I don't see why it should be impossible to use Open Hand Technique to push someone diagonally upwards as long as it is "away from you."  If this causes an extra 1d6 fall damage, so what?  The Monk spent a Ki point to do the Flurry of Blows.  An additional 1d6 is not that big a deal since you're using a limited resource to do it.