End to end encryption allows for the ends to exchange information without fear of the intermediaries leaking the information to others.

Even if it weren't connected to your identity, you may send pictures you wouldn't want seen by anyone you didn't send them to.

You wouldn't want to send forbidden thoughts if your local government was known to repress them. A government could certainly track down your multiple identities and jail you.

I'm more likely to be harmed by government corruption or poor security practices of a messaging service than by terrorism; I would rather be safe from the first two, than maybe have slightly less of the third.