Noticed you didn't mention the doctor in there, as if he/she makes a mistake, you may not be around to contest it later. I beg to differ, and think it is a perfect analogy. All of these careers (including police officers) receive professional education. If you are arrested, you can still later be proven innocent. I see no difference.
Also, if plumbers, dentists, etc., do not interact with the general public, then just who do they interact with? The difference is that the majority of officer contacts with the public are non-consensual (ie, traffic stops). This immediately builds animosity towards the officer, though he/she is only doing their job. Given that, the playing field is hardly fair, and thus you have cop-bashing, as witnessed here.
I rest my case.
