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The reason is when you pipe the file to a while loop, it actually gets executed in a sub-shell:-
cat $1 | while read line
So the scope of the variable sum value is within the while loop. This is...

such as it is (although there's a program for that, called wc :)):

sum=0
while read line; do
sum=$((sum + 1))
done < $1
echo $sum


$ cat -n myFile
1 this
2 is
3 a
...