New kit day is something that we've all experienced. Usually it's the first time you get a pair of bib shorts and a jersey with back pockets (it was for me). Before that I was wearing bike shorts and a tight fitting running shirt. When I put them on and went out for a ride for the first time with them on it felt new and different.
I felt like a cyclist.
This feeling would happen many more times (first time with clipless pedals, etc.), especially every time I would get a new bibs or a new jersey, so several times a year.
After getting on a team it changes a bit. New kit day is once a year, and signifies the beginning of a new road racing season. The old kit is worn out after a long season of training, racing, racing cross; it's likely at least a little scuffed from crashes, and stretched from being worn and washed a zillion times. Slipping on the new fabric feels silky, the colors are vibrant, and the fit is tight and exact. The season is a blank slate, and you have your training and goals ahead.
It reminds me of the beginning of the school year in high school or college - starting from a blank slate, with new clothes, books and professors, but with the same classmates and friends.
I also think it's fitting that the season begins in spring (vs Fall for school). Just as a racer spent the winter building a base of fitness, the rest of the world was also growing roots and other base structures. And just as a racer works at the top end of race fitness into the spring and summer, the rest of the world also grows at the tips of its reach: leaves, flowers, new growth.