I have so many thoughts about this! I used to be scared of dogs. Like really scared. I tend to explain it with the dog attack my mum and I experienced when I was 2 years old - the 90ies were the wild west here in Eastern Europe and there was a big free running aggressive dog in the neighbourhood we lived at (a wolfdog would be the translation from Estonian, i don't know about English) who attacked us out of nowhere. I don't know if I actually remember it or just remember the story I've been told about how my mum lifted me up above her head to keep me safe as the dog ripped into her coat. We were both unharmed but I remember her showing the coat to my grandma and it had big holes in it from where the dog jumped on her back. I was terrified of dogs as a child, possibly as a result of this.
Fast forward a couple of years and we were sledding in the park with my mum, a few of her friends, and me. I was not yet in school so maybe 5-6 years old. I sled down the hill and a small fluffy sort of dog jumped on my chest, barking. Probably it wasn't trying to scare me but wanted to play. At least that's what the owner who stood nearby seemed to think, laughing. It was a tiny dog - you know the sort, small and yapping loudly - and probably not very threatening to adults. The owner probably wasn't trying to be mean, she was just laughing about her little dog trying to play with this child and pushing it over in the snow. I was terrified out of my wits though, crying, maybe screaming. I don't remember what I did except that suddenly there was a dog on top of me, barking, and I was just in shock with fear. My mum who didn't have a sled slid down the hill on her back to rescue me, injured her spine, and had trouble walking for weeks afterwards, having to mostly stay in bed. And I remember the owner just laughing, doing nothing to stop the dog. Because it's harmless, a tiny funny thing! It's not going to bite! At least that's what I imagine she might have been thinking. (Did she think the child was screaming and crying with snot running down her face out of joy?) A harmless tiny little thing who pushed a random child over and scared her witless.
Anyway I'm mostly over it by now. I have learnt to walk by barking dogs not going to the other side of the road, to say hi to dogs and let them smell me and make up their mind about whether we're going to be friendly and mostly have no issues. I'm not scared of dogs I know well unless they're being deliberately threatening. I might like to pet your dog if it seems friendly and soft. I am cautious around dogs though and most of them can tell and are cautious in turn. I think they think I'm being a bit sus and I'm fine with that. I'll never be a dog person, but I love them as I do all animals, and if someone in my family had a dog I'm sure we'd figure it out. I much prefer small to medium size dogs though, where I feel like if I had to defend myself (or them) I could reasonably pick them up and take them someplace else. Big dogs who could jump on me and push me over or run away and pull me along make me feel unsafe though in my experience the small yappy ones can be much more likely to bite - I think they're insecure :P Anyway I'm cool with dogs for the most part, I just don't especially want one near me unless we know each other for a while or they're really chill.
People who are big dog people seem to find all of that very suspicious of me though. Like on a character level. You do not really want a dog or want to interact with dogs? What's wrong with you? How can you be a good person and not like dogs? They understand my reasoning from "childhood trauma" but what if I didn't have a good excuse like that? And as much as I try to tell that I'm not a monster, it's not like I hate dogs, nor even truly dislike them - I just wish they kept their distance until we can come to an understanding on how much contact we both are comfortable with - they still treat this as some unimaginable character flaw.
And then these very same people tend to be absolutely hateful about cats. They're the "cats are mean assholes" club when my theory is just that they have much more experience with dogs and the issue is they excpect cats to act like dogs. And then get upset when they don't. Or they have traumatised their cat (or adopted an already traumatised cat) and are now treating the cat's response whether it's aggresion or fear as "cats just being cats you know how it is". I have seen some very stressed cats whose people don't seem to realise at all that their cat is constantly in survival mode from never getting a moment's peace. And some very bored cats whose people do the opposite - thinking cats like to lay in sunbeams and sleep a lot means they don't need any attention at all.
Anyway I think this goes for animal and human interaction as well as human-human interaction: consent!
If I don't give my consent to be jumped on and licked I should not be jumped on and licked. You as an owner need to make sure that doesn't happen. If a dog doesn't consent to being patted by strangers we the strangers should honor that just as we don't start hugging random people on the street. If we can't pick up the cues from the dog we must respect their person's input. And we shouldn't touch cats either when they don't want it. Now cats tend to make it pretty clear when they're upset but are smaller than humans and can be easily overpowered. As tempting as it is and as much as I did that as a child (accidentally resulting in some cats never trusting me however much I wanted them to) that is not a great way to win a cat's heart. Would you like someone to pick you up mid-nap? Probably not. Especially not as a first meeting. Much harder to stop a cat from touching people when it wants to but it might be possible to keep the cat in another room for example, if someone is around who doesn't want to interact with them (yes such people exist). Consent! Both for the humans and the animals* We all want to be able to choose who sits in our laps or pets our hair or gives us wet kisses :D
*with exceptions if it's some sort of life or death situation or something. but you know you can find a loophole in anything - I'm not talking about "what if a dog is about to be hit by a car"