To build on what you said, the right to protection, self-protection, lies with the people.
There is no police inherent to government. Government comes in its creation without police. Just like we might hire someone to mow our lawn, we hire a police force to do the labor of our protection. Were we all wealthy, we might all have private police protecting us as do the very powerful and the very wealthy, until then, we hire our security by joining together to fund a shared security force.
Hiring police to protect us does not eliminate our right to protect ourselves any more than hiring a gardener eliminates our right to mow our own lawn.
What has happened in our country is that the government has turned our police into their enforcement branch rather than our protectors. That leaves us with only ourselves to protect ourselves.