The Gravemind at that point had integrated itself into High Charity.

Well, I know that. Was there any reason it decided to go itself, though, instead of just sending some flood in?

Likely to overwhelm the opposition. There's no clear answer in the lore. In reality, it's just poor writing.

Sad. On another note, I’ve only heard brief mentions of it. What’s “Logic Plague” exactly?

At the height of their power, the Flood corrupted everything. Life, machines, and even space-time. They corrupted machines through the Logic Plague, a digitized version of the Flood spread through logical paradoxes and persuasion. Once a machine was infected, they could spread it to other machines. Attempts to safeguard ancillas against the logic plague failed, and on several occasions, entire superluminal networks had to be shutdown because an infected ancilla accessed the network else the Forerunners risk mass defection to the Flood. The first notable example of this was 05-032 Mendicant Bias. Infecting it took 43 years however. While the spread from ancilla to ancilla is a slow process, once the logic plague reaches pandemic proportions ancillas can turn to the Flood within seconds.