Why can't furniture be counted? In Spanish it can be counted. I have a chair, a table, and a couch in my living room for instance. Therefore I have 3 furniture(s)
Because 'police' is the name of the whole service, not the job. The people who work for the police service are police officers.
To take your doctor example, it would be like calling doctors 'hospitals'. We say 'call the police' when we need help in the same sense as 'call the hospital'.
Mystery solved. By the way, are moderators and high-class users the only ones who can put up their own pictures like your cute girl over there? I want to add mine too