It could easily be something as simple as your body language
Why would a single woman read that differently than others would?
Body language is reciprocal.
If you're insecure, maybe you're afraid that she's going to be afraid, it will be reflected in your body language.
People discern how to interact with others, the emotional context, based on the information they don't realize they're picking up.
If you're telling them you're afraid of something (rejection, being judged, coming across "bad") with your body language, that's just telling them there is something to be afraid of, so they will look for danger, look for what makes them right, justify or validate that impression.
Similar to going outside and staring up at the sky. Many to most people passing by will at least glance up, and if they don't see what you see they'll look for something else to justify/validate/reward their looking up.
Why do you think "confidence" is such a huge factor for women?
"Confidence" leads to open and honest, secure, and consistent body language that is neither dominant, nor camouflaging ulterior motives.
It indicates you aren't hiding something, and what you are projecting is something that has value.
Why do you think word of mouth advertising is considered the best?
People (especially women) automatically look to others to tell them how to feel, what to think, and what to do.
They just don't generally want to believe that about themselves.
They tend to tell themselves it's "energy" or "vibes" or their "gut," when it's not really based on themselves at all and there's a lot of learned self manipulation.
Other than that:
Why would a single woman read that differently than others would?
Partly because they already have that romantic "social group" defining their situation and how they should/shouldn't respond.
It's kind of like asking "why would a person unemployed for 10 years interpret an approach by a recruiter differently than someone 10 years employed and happy in their job?"
Are single woman truly fearful of any interaction with a single man who is a stranger?
Some are, and it really does depend on context.
Could be you're interpreting their response as fear when what they're really feeling is annoyance. But based on the "metoo" and harassment climate we live in, an annoyance response can trigger "fear" body language (in order to trigger a "fear" response in you to make you feel bad for making them feel fear so you will run away, thereby leaving them alone and stop annoying them).
An annoyance response can trigger fear body language indicators (as a means of manipulating a response from you) as well as then triggering an actual fear response in order to manipulate body language to make it more clear and obvious and justify the response.
Is it a reasonable fear?
Doesn't matter if it is reasonable or not.
If you approach and the woman becomes unreasonably afraid are you going to stand there and argue with her why her fear is unreasonable and try to force her to manipulate her emotions or change her fear triggers, as a stranger?
What can a man do to make them more at ease?
That's subjective to the woman and situation, but the more you share in common in terms of culture and social training and position and communication the more you are going to naturally trigger an acceptance response.
How much of that fear is a result of sensationalized news or social media?
17 ergomacons/liter.
