Essentially, they want to honor the will of the people. The will of the people, by democratic vote, was to leave the EU.
With that in mind, they have no options that are in any way good:
1) Push ahead and exit with no-deal (economically disastrous)
2) Push ahead and exit with the proposed deal (economically bad while also not really exiting)
3) Declare it a bad idea and just don't do it (political suicide for everyone involved & creates distrust in democratic process)
4) Hold another referendum where it's going to have to be a decision between staying in or exiting with no deal (also political suicide & creates distrust).
There's no way for anyone to win here. I think the best option is for the PM to "take one for the team" (i.e. the country) and take option 3/4, knowing that it will be the end of her and her party.