There are many reasons to learn how to divide agog into syllables. Separating a word like agog into syllables is mainly to make it easier to read and pronounce. The syllable is the smallest sound unit in a word, and the separation of the agog into syllables allows speakers to better segment and emphasize each sound unit.
Knowing how to separate agog into syllables can be especially useful for those learning to read and write, because it helps them understand and pronounce agog more accurately. Furthermore, separating agog into syllables can also be useful in teaching grammar and spelling, as it allows students to more easily understand and apply the rules of accentuation and syllable division.
In the case of the word agog, we find that when separating into syllables the resulting number of syllables is 1. With this in mind, it's much easier to learn how to pronounce agog, as we can focus on perfecting the syllabic pronunciation before trying to pronounce agog in full or within a sentence. Likewise, this breakdown of agog into syllables makes it easier for us to remember how to write it.