"Pedantic" describes someone who is excessively concerned with minor details, rules, or formal correctness, often to a fussy or overly strict degree, especially when it comes to academic or technical matters. A pedantic person will correct small errors that most people would overlook and insists on precision even when it is not really necessary.
"Finicky" means excessively particular or fussy about small details, which captures this exact quality of being overly precise and hard to please over minor points. This makes option 3 the correct synonym.
Option 1, "referring to small children", has no connection to the meaning of pedantic at all; it seems to be included because "pedantic" superficially resembles words like "pediatric", but the two words are unrelated in meaning. Option 2, "teaching methodology", plays on the fact that pedantic sounds close to "pedagogy", which does relate to teaching, but pedantic itself is not about teaching methods, it is about excessive fussiness over details. Option 4, "angry", describes an emotional state that has nothing to do with the fussy, detail-obsessed nature of pedantic behavior. Only "finicky" accurately reflects the core meaning of the word.