How to print only the unique lines in BASH?

Use sort and uniq:

sort inputfile | uniq -u

The -u option would cause uniq to print only unique lines. Quoting from man uniq:

   -u, --unique
          only print unique lines

For your input, it'd produce:

eagle
forest

Obs: Remember to sort before uniq -u because uniq operates on adjacent lines. So what uniq -u actually does is to print lines that don't have identical neighbor lines, but that doesn't mean they are really unique. When you sort, all the identical lines get grouped together and only the lines that are really unique in the file will remain after uniq -u.

Using awk:

awk '{!seen[$0]++};END{for(i in seen) if(seen[i]==1)print i}' file
eagle
forest