I thought the reason was pretty obvious
Damage Control
Since EA and Bioware pissed off a lot of people like never before with the ME3 ending they are releasing the DLC for free in an attempt to minimize the loss of future potential customers. I'm sure you've noticed the amount of people stating they will never buy an EA or Bioware game again.
You can bet your ass that if there was no controversy over the ME3 ending then EA would be charging money for the multiplayer DLC.
Damage Control
Since EA and Bioware pissed off a lot of people like never before with the ME3 ending they are releasing the DLC for free in an attempt to minimize the loss of future potential customers. I'm sure you've noticed the amount of people stating they will never buy an EA or Bioware game again.
You can bet your ass that if there was no controversy over the ME3 ending then EA would be charging money for the multiplayer DLC.