1st: Welcome home, brother. 

2nd: Community policing requires that LEOs be a part of the community. That they know & are known by the community. The beat cop of yore is an excellent example. But today's LEOs have too much territory to cover and too little time for community engagement. They spend their shifts responding to calls and filling out paperwork. Most people only interact with LEOs in crisis situations where tensions are high for both parties.
 
3rd: Your analogy to an occupying force is apt. Without a personal investment in each other between the public and LEOs, it does become US vs. THEM. Even if they are doing what we ask them to do - maintain law & order. 

4th: Because LEOs operate in crisis mode so often, any hesitation on the public's part is viewed as a threat to their authority, to their ability to maintain order. Recent events lead this to a threat on their lives. Situations escalate quickly.