@The:
Who thinks Luffy will fight BM? Personally, I think so.
She has the keys to Sanji's explosive cuffs to make sure he can't escape or so Luffy can't just carry him out of Totland. Plus, Luffy said that he's fed up with running away from every formidable opponent he runs into and is willing to fight anyone who's chasing after him, that's why he fought Fujitora, Cracker, and in the near future, Kaidou (with help).
This is just my two cents on the subject.
I think is a given that they will fight, what is uncertain is how will it end. Luffy is struggling hard against one of the commander, so the idea of defeating the yonkou herself seems absurd. A lot of people are certain that Big Mom will not be defeated this arc, while i agree that this is overall a more likely outcome i would not discard the possibility of Big Mom defeat either.
If we think about the past adventures even the fight with Crocodile was desperate, his bounty was almost three times Luffy's own and he was a shichibukai, while the most Luffy did then was defeating a 20 mil Arlong, Wapol and Mr.3, and as it was to be expected Luffy was totally trashed in their first encounter. And though he was still defeated in their second round, at the end he won.
If we now reflect on the cards on table here i think the situation is not that desperate. It's now confirmed that Capone is planning something shady against Big Mom, and he doesn't seem a man that would do something reckless, he must have some concrete plan that could inflict her a great deal of damage. As for the Vinsmokes we still don't know where their allegiance really stand, their so called mythical evil army has yet to be revealed, and there must be a reason Oda introduced it in the first place.
If each of those parties would turn on Big Mom the chances would drastically increase.
Those are my thoughts on how BM will be defeated, if she will be defeated at all.