Interesting. My answer is going to be a bit all over the place, but stick with it, because the question you're asking isn't the issue you need to address.
Why Everyone is a Potential Threat
The issue with potential threats is recognizing a threat and not fabricating a worry. When martial artists begin training, we're thrown into a situation where, for a few hours each week, we are attacked again and again and again. We are forced to throw around and to get thrown around by people that we then stand up, shake hands or bow, and do it again. Then we go home.
Psychologically, this is a bit like Sub- and Top-drop in BDSM – a certain level of aftercare is necessary to bring an individual after a scene back to the real world. When my training group started going to dinner after class and talking about our experiences, we all improved. Incidents of fighting outside of class dropped. Overall stress levels decreased. Why? Because we were unwinding.
So you go to class and get your butt handed to you for a few hours then you go home; what happens? Maybe you sit up for a few hours, watch an action movie, or you do a project until you can sleep. Why? Because you have stress hormones coursing through your body. Let's say you go to sleep still amped up; what happens? You have stress dreams and you wake up most of the night. Your levels of cortisol and norepinephrine don't decrease, which makes you tired and edgy, and actually causes you to stress more. So, after a few days of this, you have a baseline stress level that's higher than the average person. Then you go to training again, burn off some nervous energy, feel good while you're doing it, then feel edgy again the rest of the week.
Now, meanwhile, your stress trigger is becoming people that you know and trust. If you know and trust the people that you're training with (the ones who are getting your blood pumping), you're going to trigger harder off of people who you don't know.
Recognizing Actual Threats
Our brain is extremely adept at analyzing patterns. So when your partner glances at a particular portion of your body, your subconscious mind registers the glance, and prepares your body to move as you've trained.
Now, when someone on the street gives you a similar glance, your mind is saying "This person is a threat - I know this pattern!". Train longer and you refine this pattern; no longer is the glance the warning you need, but the fist flying toward you, because you'll know you have plenty of time to move.
Martial arts are as much about avoidance of threats as they are about combating those threats. When your brain starts to acknowledge the patterns that lead you to those actual dangerous moments, you will begin to avoid those situations more fully. If going down a dark alley leads you to getting mugged, you'll stop going down dark alleys. This same pattern recognition (in a primitive form) is why prairie dogs always hide when they see a shadow.
You must learn to train your body and mind to recognize reasonable threats from fears, and learn to react appropriately. This is going to start by breaking the pattern that you've already developed – namely, that everyone is a threat.