merge two files, first line from first file followed by first line from second file

It's a job for paste:

paste -d'\n' f1.txt f2.txt

Example:

$ cat foo.txt 
some text line 1
some text line 2
some text line 3

$ cat bar.txt 
A1
A2
A3

$ paste -d'\n' foo.txt bar.txt 
some text line 1
A1
some text line 2
A2
some text line 3
A3

Yes, you can do this using one while loop and read through the two files using read.

#!/bin/sh

while read file1 <&3 && read file2 <&4
do
    printf "%s\n" "$file1" >> mergedFile.txt
    printf "%s\n" "$file2" >> mergedFile.txt
done 3</path/to/file1/file1.txt 4</path/to/file2/file2.txt

You can use echo instead of printf. The results are in mergedFile.txt If the files you are processing are not huge, perhaps the above is easier and more portable than most solutions.