Mrs May has convinced herself that as prime minister she has to leave some form of legacy. This has, in my opinion become obsessive and all encompassing of her tenure at number ten. It is saddening to see someone so blinkered to her inability to provide the solution. Her stubbornness makes her look foolish and arrogant.
I don't think it's that. I think it's that she is an ardent believer in the Conservative Party, and as such cannot be the leader that allowed it to split. Ever. So when the ERG have come to her and said 'do as we say or we split the party / the grass roots party is on our side', she's done as they said. The problem is of course that this schism has been running in the party for at least 30 years, and is now being forced to a head. So there's probably no way she can avoid a split. It's all too late. On the other side, Europe see the folly of her stance, and have thus given her a pretty crap deal on a 'take it or leave it basis'. But she can't leave it, as that might split the party, either through no deal or no brexit, so all she's left with is taking it.
Which is why her plan for a long time now has been to just run down the clock, force the country to a cliff edge, then say it's either my deal or the chaos of no deal (that the ERG would quite like). Hence today's announcement of a delay in the meaningful vote right up to the 11th hour, ostensibly for further negotiations. A stance which is becoming increasingly surreal, given the european negotiators have been saying for ages that there is no renegotiation to be had.
They know full well what her personal mission is, and how it's ruining her and her party, and thus see no reason to renegotiate. The sad irony is that the tory party probably is going to split over this anyway, or at least be no more united than it's been for a while now, so her only hope of not being the leader that presided over a party split is not to be the leader when it happens. But she's also not the sort to give up. The perfect storm of poorly suited character traits.
Basically, she's entirely the wrong person for the job, but when the post-brexit leadership election happened, everyone tried to dive out of the way of having to lead the brexit process, leaving her the only person foolish enough to still be standing. I've always thought that she's one of those types very common from Oxbridge, academically brilliant in certain fields, but crushingly bad at life in general.