There are a lot of people who continue to spread the FUD around Messenger, and it is making me crazy.
Anyone who thinks they have privacy on a third party service needs a reality check.
As Scott McNealy said in 1999, "You have zero privacy anyway. Get over it." Anyone who still believes using a service someone else owns (especially for free) entitles them to privacy is sadly mistaken. Most services will try to do the right thing, but there will always be a chance of an accidental data breach or hack, even from the most trustworthy services. You can only hope that the company wants to do good by the consumer.
Simply put, if you don't control it, you can't expect it to be controlled for you.
There are two primary complaints I've heard during this whole Messenger debacle.
The first is that Messenger terms now allow them to spy on you and you can incriminate yourself by using it. First, companies are required to comply with law enforcement if they want to do business in this country. Second, if you are doing anything illegal, you shouldn't be discussing it on something someone else owns anyway. This has always been the case with your telephone, text messaging, etc... that's just common sense.
The other complaint is about unrestricted access to your camera and photos and contacts. Once again, that's nothing new - you authorize your apps all the time for access. Let's take some popular apps for example: Snapchat? You probably authorized it for camera, photo album and contact access. Apps need photo album access to be able to get past photos. They need camera access to take pictures/videos inside of the app. Instagram? You most likely authorized those for camera and/or the photo album too. You probably authorized LinkedIn to your contacts. You most likely authorized the original Facebook app to your camera and photo album (otherwise you can't post any images from inside the application!) - you probably even authorized it to access your contacts.
I feel bad for Facebook having to deal with such unoriginal claims. Yes, it sucks to have to install yet another app, but they have reasons for it and it works well in conjunction with the original Facebook app. It's free, and it isn't a space hog, so there's no real "cost" associated. Battery drainage is the only complaint I consider to be reasonable.
Just remember - nothing is truly private. Even your encrypted end-to-end messaging - someone can take a screenshot or save it and share it. It comes back to what Jon Voight said in Enemy of the State, "The only privacy that's left is the inside of your head."