I'm going to attack the argument from another angle.
A Church, whether christian or otherwise like any quasi-community entity needs followers. These followers tend to follow a religion but then also associate with a particular church. Now if the goal of churches is to get more followers, then the way to do that would be to increase following of the religion and in particular in such a way that people would associate more with that church.
You collect followers by being more appealing, and unfortunately the churches best weapon for this is fear. "Join us or burn in hell!" is the message heard most clearly. Some even say "Church every Sunday or burn in hell!" This fear is not for the "salvation of the "people" but mainly to get more followers.
They also furthur highlight their own morality, leveraging it in such a way that the followers feel they are superior to others just for following a religion. "I'm better than you because I'm a Christian." can often be heard by the religious. The association with a particular church helps people feel more important than their fellow man, and helps the church retain followers by painting others as lesser.
Now if you take this whole mess of fear and superiority, and compare it with empathy, Empathy involving putting yourself in anothers shoes, and seeing from their point of view, you can see how empathy will totally shatter the illusion of fear and superiority. The truth that everyone is just like everyone else would completely shatter the feelings of superiority that are taught by a church, and the fear of an imaginary condemnation would break when the only thing worse than damnation is being afraid for the whole time you are really alive. Empathy a contributor for awareness, and fear and superiority don't last long in the light of such awareness.
So the sole reason why churches don't teach awareness is because they would lose followers, and without followers the church would cease to exist. All the churches that teach compassion have long disolved, and become just religions. A church can't teach empathy and still exist.
It's also why you see many empathic, compassionate religious people who don't go to church. There's no church that teaches it, and really no need for one.
