The backstop was an EU proposal, suggesting that NI remained in lockstep with the Cusgoms Union and Single Market. It was initially rejected outright by May because, and if you recall, it "would put a border diwn the Irish sea", and effectively break up the union.
The background to that was that EU had placed (at Varadker's prompting) the "hard border" issue as one of the three critical initial issues which, until dealt with would preventvthe EU even discussing other matters .... like the politically hot matter of cituzen's rights in the other's pist-exit territory whuch May had bern trying to get dealt with since before art.50 was even invoked, only to be met with point-blank refusal from the EU, until their three hot topics were dealt with.
Which is when that EU proposal for the backstop was put forward, and May agreed to the principle.
Then even that blew up when the EU's chief negotiator, Barnier, put forward the text of how his team interpreted that, and that legal text was immediately rejected as it "broke up the union", and the EU dug their heels in and again refused to move on until this was resolved.
At most, May caved in in order to try to move things on, as "the clock was ticking".
I'm on record as being no fan of May. I detest her, and in my view, she personally is the single biggest reason we're in this mess now, not least because she never has agreedcwith Brexit and I have my suspicions about how much of her incompetence is just that, and how much is deliberate, to engineer just juch a mess.
But to say she put the backstop in is tantamount to blaming the bank cashier for putting money in a robber's bag when the robber has a shotgun pointed in her face.
The EU set it up. They made it a priority, refused to move on until it was dealt with and then rejected every other option, including the "alternative arrangements" they are now claiming will avoid a hard border in the "increasingly likely" event of no-deal, like checks done miles behind the border.