I'm not sure why those who cycle sometimes come across as a bit touchy. Surely even they get irritated by cyclists sometimes.
I've considered myself a cyclist almost all my life. I used to cycle to work all year round and at weekends for pleasure too.
There's always been a car in the family, but registered to my wife (I've mostly owned motorbikes) so, like many, I've been stuck for what seems like ages in a car behind a couple of dozen cyclists riding two or three abreast at about 15mph (or less). I was a cyclist driving a car and swearing at cyclists... is that so unusual?
As a walker I sometimes get irritated by cyclists. I hate the silly 'ding', which means what exactly? You're behind me? You're going to pass me? You want me to get out of your way? I don't think I've had a bell on a bike since I was riding three-wheelers as a child. I've never needed one. I call out "Good morning!" or "Excuse me please" or similar, which I think is much more polite than the meaningless 'ding'.
But I would also make a plea for tolerance for cyclists. I cycled on paths through woods and across fields well before I called myself a walker. Stiles and gates could be a pain, especially if the family was with me and I was the one having to lift four bikes over a fence. My point is... I knew nothing about rights of way and I would ride my mountain bike along any path that looked promising. I've been shouted at by farmers, got off my bike and pushed it, and got back on when I was out of sight. Nowadays, of course, I'm as quick to judge as anyone - if a cyclist is on a path that I know is a footpath, then I'm likely to point that out in a somewhat self-righteous and entirely hypocritical way.