I'd like to know the circumstances & inspiration that led to its creation, and the context it was created in.
The Cherokee Syllabary was one of many manifestations of the Cherokee trying to establish themselves as a "legitimate nation" as a means of self-preservation. The Cherokee were one of the "Five Civilized Tribes," southeastern Native tribes that adopted many of the strappings of Euro-American civilization in an attempt to become legitimate in American eyes. By mimicking Euro-American standards for civilization, the Cherokee and tribes like them hoped to better defend their land claims to the American government.
The program was somewhat planned, but also emerged very gradually. White men married into the leading families of the Cherokee tribe to get access to their farmland and the children of these unions considered themselves fully Cherokee. They inherited their fathers' farms, often slave plantations and many of this mixed-blood elite believed in the need to mimic the Euro-Americans not only for their own economic prosperity but also for legal foundations for their land claims. The Cherokee had a legislature, court system and Supreme court, taxation, an elected chiefdom that was functionally a presidency, western-style towns with brick buildings, etc.
It is very important to note that the Cherokee were not trying to erase their heritage or their identity. These efforts to modernize were a kind of nationalism. The full-blooded majority of Cherokee still considered the mixed elites to be fully Cherokee. This nationalistic sentiment was not restricted to the mixed elites, however, as Sequoyah demonstrates. We are uncertain about whether or not Sequoyah was a full-blood, but he was certainly not an elite and grew up speaking only Cherokee. Sequoyah, a silversmith, grew to appreciate English script as a means for communicating information, stories, and culture. Sequoyah created the syllabary as a means of preserving Cherokee culture. This was not done in opposite to the civilizing program of the mixed elites, but as a consequence of the same desire to preserve Cherokee culture.
The mixed elites published a bilingual Cherokee newspaper called The Cherokee Phoenix and installed an education system that taught Cherokee children in their own language using Sequoyah's syllabary. The syllabary and the education system were both extraordinarily successful and the overwhelming majority of the nation achieved literacy in a very short span of time.
Sources:
Ellen Cushman. Cherokee Syllabary: Writing the People's Perseverance. Norman, OK: University of Oklahoma Press, 2013.
Fay A. Yarborough. Race and the Cherokee Nation: Sovereignty in the Nineteenth Century. Philadelphia: University of Pennsylvania Press, 2013.