Honestly I don't find that hard to understand what's going on.
Basically, May negotiated a deal with the EU but the UK Parliament does not want it, mainly due to the so-called backstop. The backstop emerges because May has a red line that the UK must leave the single market and the customs union, and this is difficult (if not impossible) to reconcile with the Good Friday Agreement, which forbids a physical frontier at the border between the Republic of Ireland and Northern Ireland.
The fact is that, as Northern Ireland is part of the UK, it is simply impossible to make the (whole) UK exit the single market and customs union while honoring that agreement. If you place a border in Ireland, you violate the agreement. If you don't place a border in Ireland, then obviously goods and people can circulate freely, so Northern Ireland is effectively part of the EU for customs union and free movement purposes.
This is the very simple (not complex at all) reality that the UK government and parliament have been voluntarily ignoring all the time. To try to reconcile the contradiction, Theresa May proposed the so-called backstop: basically, Northern Ireland stays in the customs union until a technological solution is found that allows to have a non-physical border (yes, I know, bollocks. It won't happen. But Brexit proponents are like that). The EU signed this because May insisted and because why not, if no such miracle solution is found then Northern Ireland remains in the union so it's no problem for the EU. But the hardline Brexiteers in the Tory party (rightfully) pointed out... well, exactly that: that the backstop would imply that Northern Ireland would stay in the customs union forever. Hence, the process is stalled because May's deal has no consensus in parliament, but there is no consensus either for Brexit without a deal or for cancelling Brexit (all of this has been voted this week, with the result of "no" to everything).
If parliament keeps voting no to everything, then the default result is no-deal brexit.
Honestly I don't think there is that much complexity. It's just a very simple problem: that you cannot have Brexit including an exit from the customs union that involves Northern Ireland and the Good Friday agreement at the same time. That's pretty much all there is to it. If it seems complex, it's because the UK politicians don't want to admit it and just keep running in circles.
That particular problem is indeed 1) very straightforward and 2) unsolvable. It's a major driver of the chaos. But that's just it - the situation is chaotic. There are many sideshows and complexities, and the upshot is that nobody really has any idea how it's going to play out. As shown by the elaborate diagram linked at the top of the page.
That problem is a sufficient condition for the chaos, and what has caused it. Without that problem, there could be consensus or not, and there could be other things to discuss, true. But that problem is enough to understand the current chaos.
You know what's funny? That even if the UK parliament never agrees and there is a no-deal Brexit, that problem doesn't disappear. In the event of a no-deal Brexit, the UK will be in violation of an international treaty (the Good Friday agreement), and the EU (and even the US) will ask them to honor the treaty. Fun times, indeed.
I wouldn't make any bets about what the US would do, sadly. I get the sense that the DUP and most people pushing for no deal actively want to tear up the Good Friday agreement (and blame the EU, even if that makes no sense).
I think this issue leads people to overestimate how much support the EU is giving to Ireland. How much they will support Ireland is still to be seen, but for now it seems to be more like "wait, agreeing to do what you already agreed to do is supposed to be the easy part; how can we negotiate with these people?"
IMO, the updated flowchart is way too optimistic. I don't see any reason to suspect parliament won't keep doing what it has been doing, either nothing in particular and crashing out or, more likely IMO, finding a consensus around an impossible plan, crashing out, and blaming the EU for not accepting it. If they were actually going to do anything different the time for that seems to have come and gone a long time ago. "Revoke article 50 if we can't come up with a plan" went down to a huge defeat Thursday as it has previously.
Edit: Looks like I should have checked the news first, sounds like there may actually be a general election. Edit2: Maybe not as clear as the headlines suggest.
It's not unsolvable, there are detailed proposals for how to solve it and after announcing loudly they would never work, the EU recently changed its mind and announced they'd already started preparations for it.
The only reason the Irish border is being described as "unsolvable" is because that suits the agenda of people who want the referendum to be ignored (as in Europe they always are).
Basically, May negotiated a deal with the EU but the UK Parliament does not want it, mainly due to the so-called backstop. The backstop emerges because May has a red line that the UK must leave the single market and the customs union, and this is difficult (if not impossible) to reconcile with the Good Friday Agreement, which forbids a physical frontier at the border between the Republic of Ireland and Northern Ireland.
The fact is that, as Northern Ireland is part of the UK, it is simply impossible to make the (whole) UK exit the single market and customs union while honoring that agreement. If you place a border in Ireland, you violate the agreement. If you don't place a border in Ireland, then obviously goods and people can circulate freely, so Northern Ireland is effectively part of the EU for customs union and free movement purposes.
This is the very simple (not complex at all) reality that the UK government and parliament have been voluntarily ignoring all the time. To try to reconcile the contradiction, Theresa May proposed the so-called backstop: basically, Northern Ireland stays in the customs union until a technological solution is found that allows to have a non-physical border (yes, I know, bollocks. It won't happen. But Brexit proponents are like that). The EU signed this because May insisted and because why not, if no such miracle solution is found then Northern Ireland remains in the union so it's no problem for the EU. But the hardline Brexiteers in the Tory party (rightfully) pointed out... well, exactly that: that the backstop would imply that Northern Ireland would stay in the customs union forever. Hence, the process is stalled because May's deal has no consensus in parliament, but there is no consensus either for Brexit without a deal or for cancelling Brexit (all of this has been voted this week, with the result of "no" to everything).
If parliament keeps voting no to everything, then the default result is no-deal brexit.
Honestly I don't think there is that much complexity. It's just a very simple problem: that you cannot have Brexit including an exit from the customs union that involves Northern Ireland and the Good Friday agreement at the same time. That's pretty much all there is to it. If it seems complex, it's because the UK politicians don't want to admit it and just keep running in circles.