I understand your question the way that you want all lines which appear in only one of the files, not both, and disregarding the line order.
I also assume we compare the files
f2.txt. Insert your respective names instead.
Using Bash, you could do it with two loops, where each processes one file and checks for each line if it appears in the other. This approach is not very efficient, but it should work:
# This loops over f1.txt and searches each line in f2.txt
while read line ; do grep -Fxqe "$line" f2.txt || echo "$line" ; done < f1.txt
# This loops over f2.txt and searches each line in f1.txt
while read line ; do grep -Fxqe "$line" f1.txt || echo "$line" ; done < f2.txt
Both loops together produce the desired result. Each for itself only checks for lines in one file that don't appear in the other.
A neater solution could be written e.g. with a short Python one-liner:
python3 -c 's1=set(open("f1.txt")); s2=set(open("f2.txt")); print(*s1.symmetric_difference(s2), sep="")'
This uses a Set data structure, which only contains unique values and allows set operations like "symmetric difference".
Note that using both solutions, if any of the files contain duplicate lines, these are ignored and handled only like a single occurrence.