Why the heck would Law choose to go after Kaido??Why not Big Mom??
Compare the Beasts Pirates to the BigMom Pirates. Which crew is more dangerous?
The Strawhat Pirates are known for causing chaos, just look at the condition of Totland, and this is only half of Luffy's crew. Imagine if the rest had tagged along. Bege's assassination plot came somewhat close to actually taking out BigMom, if another brilliant schemer like Law had collaborated BM would be dead already. Infact why couldn't they just poison the cake and then blame it on the chefs.
Also, Dogtooth is the only Sweet Commander who stands any chance against Jack, who is presumed to be the weakest Calamity. Just imagine the others like "King". Her security is faulty, with a proper route, as supplied by Pudding, you can sail all the way through Totland undetected and those sea slugs are a waste. Big Mom, though she is powerful, is mentally unstable. Not to mention Kaido is said to be the strongest creature and is shown to be practically unkillable and is obviously stronger. He also has an army of 500+ savage DF users and the Shogun to back him up.
I'm sure if the Strawhat and Heart pirates just waltzed into Totland, met up with Pudding, Jinbe and Bege and formulated a plan they could kill Big Mom with half the effort it would take kill Kaido. They stand no chance against Kaido or Blackbeard and Luffy would never target Shanks. Big Mom is the easiest pick. Kill any of the Yonko and you're getting the same glory.
Can anyone justify Law's reasoning here?
I concur with Love Cook. You are making a ridiculous amount of assumptions here, most of which are either complete baseless or can be considered outright false.
1) We barely know anything about the Beast Pirates, but the few crew members we do know of by no means have shown to be more dangerous than the BM Pirates. Considering we know more of the BM pirates and that networking is their forte, objectively speaking it would make more sense for them to be much more dangerous.
Statement: false
2) Having had all the Strawhats here doesn't automatically mean they would have been more successful, the whole reason only half of them were here was to avoid attracting too much attention. You could just as well reason that they were so successful because only a few members were there.
Statement: baseless
3) Bege had been scheming for nearly two years. It's not because Law is intelligent that he suddenly can make a difference when he's thrown last minute in a complicated situation. Law was also allied with the Strawhats to take down Kaidou, not BM. For him this was mostly a private Strawhat-affair that did not involve him.
Statement: baseless
4) BM can nearly eat everything. She devours souls and even ate an entire group of clothed, living people when she was a small kid. Even though it's not outright stated that she's immune to poison, I think it's safe to assume that's kinda naive to think that merely poisoning here food would have any affect on her whatsoever and that they could just blame someone else for it.
Statement: false
5) You don't know if Jack is the weakest commander, that's pure speculation. Personally I'm more inclined to believe he's the 2nd strongest of the Three Calamities. You don't know either how well Cracker and certainly Smoothie, whose battle style is still unknown, would fair against Jack. We don't know either who the other Calamities are. That one of them would be named "King" is still nothing more than a hypothesis based on the running card-theme, which isn't applied uniformly. Some even say that "King" refers to Kaidou.
Statement: baseless
6) Pudding was their enemy for the most part of this arc and the main reason the Strawhats got so far, was because they allowed it and the only reason the slugs were out of commission, was because the Strawhats were aided by the Sun Pirates. This was a factor that could ever only work for the Strawhats. This is not something everyone can just replicate.
Statement: false
7) Kaidou is far from being sane himself, you shouldn't put too much value on his nickname either and unkillable doesn't mean unbeatable. It has even been stated he has been defeated numerous times before. The fact that there's some kind of a non-aggression pact between all the Yonkou and that Shanks somehow was able to keep Kaidou at bay during the Marineford arc, shows that in the least all of them are aware that picking a fight with another one might not and up favorably. So your "obviously stronger" statement is rather questionable.
Statement: false
8) And BM has hundreds of children, many of which are either DF users themselves and/or have additional combat skills. Those children then are often married off to influential and/or strong individuals from a variety of races, which allows BM to have their fighting strength at her disposal. On top of that she has her regular crew members and then an undefined amount of creatures and objects that were given a soul and are bound to her. So it's open for debate whose army here is the strongest. You don't know anything about the Shogun either. It's not because the Shogun and Kaidou have made an agreement that suddenly the latter can use the former's military strength. The way how it has been portrayed so far makes it seem this is a Wano-affair, not some kind of parent-child relationship and even if that would be the case, as said BM has been doing that for decades.
Statement: baseless
9) Saying that they could have just waltzed in there and would have yielded better results is utterly preposterous. This is a Yonkou we are talking about here. You seem to have completely forgotten the contextual frame of the entire story.
Statement: false
10) Again you are dealing with a Yonkou here. It doesn't matter which one you decide to take on, your chances to succeed are low by default. Law made this clear from the very beginning. There is no easy pick here, this impression you have that BM would have been easier than any of the others is not true. You are basing that on elements that are not universally applicable and known. You pretend that suddenly everyone can just galavant into BM's territory, while it has been clearly shown that is not the case. You pretend that Pudding is everyone's ally, while only at the climax of the wedding she suddenly became love struck.
Statement: false
The fundamental condition of the New World is: either you join a Yonkou or fight them and what you do depends almost solely on the situation you are in and the info you have. Apoo originally decided to take down Shanks, but then suddenly comes into contact with Kaidou. Next thing we know he's part of his crew. Something similarly most likely happened with Bege where the Yonkou he first met was BM and by joining her he could gather information to formulate a plan to take her down.
Law on the other hand was familiar with DD and had a lot of knowledge about his affaires and transactions, including those with Kaidou. Considering his animosity towards DD he could also hit two birds with one stone: by pitting them against each other one of them would be destroyed while the other one definitely would be weakened to some degree. That Law decided on Kaidou made absolute sense as putting aside that the picture you are drawing here about BM being easier is nonsense, Law knows more about Kaidou than BM. He was much better positioned to focus on Kaidou than BM.
Uroge/Bege/(Luffy) - Tried taking down BM
Apoo/Hawkins/Kidd - Tried taking down Shanks
Law/Luffy - Tried taking down Kaidou
For them there is no easy Yonkou. You give the impression that you think this is some kind of game with four bosses where every player has the exact same information, skills and equipment and that a pecking order can be establishment among the bosses, but that is not the case.
