Blackbeard is going for Buggy now that he knows he is no longer protected by the World Government.
This may even be the reason for the confrontation between Blackbeard and Shanks that Oda teased in Marineford.
Blackbeard’s motivations
We must remember that Blackbeard is not like Luffy. Blackbeard does not care about freedom and adventures. He has a goal: to become the Pirate King and he will do everything to get there. For instance, if Blackbeard was in Luffy’s position with Rayleigh in Sabaody, he would have asked him where is Laugh Tale whereas Luffy refused to hear anything.
So, this means that Blackbeard is probably not the type of guy who would chase all four Road Poneglyphs, manage to read them and then eventually would find Laugh Tale. If there was an easier way to reach the place, he would take it without thinking twice.
But who knows how to go to Laugh Tale? The Roger Pirates only. But all of them are among the best pirates of all times… except one: Buggy.
Unfortunately, Buggy was a Warlord from the moment Blackbeard became a major player to chapter 956, meaning he was protected by the World Government. Capturing him at that time would have been too dangerous. But now, there is a weak pirate in the New World and Blackbeard believes he knows where Laugh Tale is (even if the reader is not sure about this part).
Textual evidences
Chapter 956: This is the most important one. In this chapter we learn that the Warlord system is now over and the Marines want to capture the Schichibukai. In the same chapter exactly, Blackbeard says he will not let the Marines have it. I believe we can assume he is speaking of a Warlord and knowing what we know about the past of Buggy, it’s gotta be the clown.
Chapter 966: We see Blackbeard facing Shanks and Buggy. Of course, we know something will happen between Shanks and Teach but Oda chose to include Buggy in the panel. Maybe, Buggy will play a role in Blackbeard and Shanks’ story.
Latest Chapter: Shanks promises Buggy they will one day go to Laugh Tale. But I don’t see any reason Buggy would today go willngly to Laugh Tale when we know that he is not interested by the One Piece. He may well be forced.
Finally, we know something is going on between Shanks and Blackbeard. One day, these two guys will fight as foreshadowed by their Marineford meeting or the fact that Shanks warns everyone of Teach.
Buggy may eventually be the casus belli, the reason why Shanks will fight Blackbeard. For his friend. Because ultimately, all is about friendship in this world. From this point of view, one may even argue Blackbeard would capture Buggy only to attract Shanks in his island but I do not really see it that way.
*Theory by Destofor