Why did the bald eagle become a national symbol?

No year. The bald eagle (a symbol of the US) appeared on the reverse or BACK side of all circulating US quarters issued from 1796 to 1974 and 1977 to 1998.

Quarters minted during 1975 and 1976 all carried the dual date 1776-1976 in honor of the Bicentennial and featured a striking image of a colonial drummer boy.

Beginning in 1999, quarters have carried images of states, territories, national parks, and other historic sites.