Even after observing eggs coming out of Mama Birds, and after discovering that newly emerged eggs were mostly liquid inside and tasted good, there was still a bit of mystical, magical, miracle about them. Eggs came to be symbols of rebirth, of new birth, and were taken up as symbols of the Spring Equinox and Spring Festivals.
Fertility rituals were performed around the time of spring planting to ensure a good crop, and during the spring mating season of prey animals for the same reason. Rabbits, even then, were notable for their fecundity and they also became symbols of the season.
Along came the Christians, trying hard to gain a foothold with the common people, the country people, the "pagans". "Our religion is just like yours. See how we use the same symbols?" The problem with borrowing someone's symbols without also borrowing their underlying religious significance is that mix-ups can occur. And so we have the Easter Bunny hopping around and bringing eggs to good children.
Don't get me started on Christmas or Halloween!