When you are doing this:
The whole file is being printed because grep doesn't recognize 'cr' as line endings. You don't see the whole content because you are printing crs the lines get overwritten.
$ grep This testing2.txt
You can see what is going on if you do:
I hope that points you in the right direction.
$ grep This testing2.txt | od -a
0000000 T h i s I s M y S e a r c h S t
0000020 r i n g cr T H I S I S M Y T E S
0000040 T I N G S T R I N G cr nl