THIS!
@Winterysun thank you SO much for posting this thread. I have been wanting to post something virtually identical for several months now. Just haven't got round to it.
I have the same odd and baffling 'issue.'
I started walking a lot some 2 years ago after I discovered fitbit, and love the achievement of getting 15 miles a week walking in. Some weeks I get more.. (20 miles some weeks)
In December, I walked to a Christmas Fayre at a place 1.5 miles from me. I got my backpack on - with my water, my phone, my purse, and a couple of bits of fruit to munch on. I was halfway there, and I stopped to have a swig of water, and a woman I had never met stopped her car by me, and said 'are you going to the Christmas Fayre?' I said 'yes.' She said 'hop in, I'm going there!' I said 'oh no it's OK thank you, I am waiting for a friend. I am meeting her here... by this sign here!' (I said this because I know how offended people get when you say no for nothing! And insist you get in!)
So she drove off. A wee while later, I entered the grounds of the place where the fayre was - even though it was still another 7-8 minutes walk, and ANOTHER woman (who I had never met before) stopped and said 'get in, I'll give you a lift to the fayre.' I said 'oh it's OK thanks, I am fine walking.' She said 'oh do get in, I'm going there and it's freezing!' I said 'no thank you! I am OK walking!' She just drove off.
No acknowledgement at all. Clearly pissed off that I had refused her lift. I was looking at a stall when I got there, and this same woman appeared (as I was chatting to the stallholder) and said 'I offered this woman a lift in my car, and she REFUSED!' Looked really irked and annoyed. I was like
The stallholder lady said 'maybe this lady likes walking.' 'Hmph' said the woman, 'it's 2 degrees out there, how silly to be walking in this weather!' I am in my late 50s, I don't need to be talked down to by some fucking random like I'm insane, just because I want to walk.
One more... The other week, I was walking from a neighbouring village, and it was a mile back to my village, and a man I have never seen before stopped next to me in his car, and said 'you going up to Upton Lee?' I said 'yes' (obviously, as the road I was on only goes that way!) He said 'hop in, I am going there.' I said 'no thanks I am on a walk, and haven't got my steps in yet. I need another 2000 steps for my daily quota.' And I smiled and said 'thanks anyway!' 
Honestly he looked at me like I had shit in his mouth, like >>>
Then he drove off. Said nothing, just glared at me!
I was like
Like why the FUCK would I get into a car for a lift with a man I have never met or seen before? Why would I even get into a woman's car who I have never met before? They are all strangers. Why would I put myself at risk?
I rarely get people I know asking me, as they know I am a walker. They see me all the time, tootling around, walking up to 20 miles a week around the area/the fields/the pathways and country roads...
But yeah, I feel ya @Winterysun !!! As this poster said, some people can't fathom that other people like to walk. Why be offended though? Weirdos!