Frankly, how did you feel after listening to the song? Actually, as this is my imagination, but, this adult man (who wrote the poem) is thinking about his old hometown along with childhood memories when he was with his mother.
On this song, he's remembering now that the small child was carried on a back of his mom. Or, when he became a school boy, he might have tried catching the insects spreading all over the red sky.
Red dragonflies are filled with the red-colored sunset but in a certain period of fall, which doesn't change as seasonal tradition over decades. That's why this particular view reminds this man and other adults of sweet memories in fall. Many people live far from their parents following marriage, taking a job or other life-changing occasions.