I grew up with a very bad spider phobia which I can attribute to two such formative experiences. I also had the bad luck to grow up in a country with big spiders. Every time I walked into a room the hairs on the back of my neck would rise up in case there was a spider by the light switch or above my head (there seldom was, but that's no help to a phobic).
This persisted through to adulthood. Then something happened that changed it all, for ever.
I parked my car in the garage and saw a big spider (yes, size of your hand African spider) dart behind some timber. I knew this was going to cause me real phobia problems just going into the garage again. I could see it behind the timber, so I got a high pressure hose and washed it out into the open to kill it. But when I saw it, all bedraggled and wet, legs curled up defensively, I couldn't suppress a spark of empathy. I was hurting it, not because of anything it had done to me, but because I had a problem.
Instead of killing it, I found myself coaxing her (yes, it was a her now, not an it) into a small aquarium - with the aid of a very long stick it must be said. The top was sealed with cling film, with air holes punched through it of course.
Two things followed from this.
The first and most obvious was that I could bring myself to look at the spider in safety. Initially in small doses, then in more detail. She was actually rather beautiful. The closest I can get from an image search is that she was probably a Baboon Spider. Her abdomen was covered in grey and beige fur, as were her legs, but banded with yellow underneath. I think this was warning signal because the bands became visible if she reared up.

Second, I had to feed her of course, usually grasshoppers shoved through the holes in the clingfilm. I don't know how much spiders drink, but from time to time I would "mist" her with a hand plant spray. This had an extraordinary effect on her. She would begin an elaborate cleaning routine, much like a cat. With the underside of her foremost legs she would comb her whole body, systematically. Then she would pass those parts of her legs through her jaws to clean them, then continue with the combing. That really was fascinating to watch.
I never did have the courage to handle her. I wanted to, but unlike the fat and lazy kind of tarantula she was very alert and quite fast. I just didn't know if she would be alarmed enough to bite. Venom was not the problem, but she had some pretty significant mouth parts.
Then the final chapter. One morning she was gone. In the clingfilm was a gaping hole. Ooops. The Houdini trick. I wasn't counting on that. I looked for her, but no luck. Well done me, I thought. Had a big spider in the garage. Now I have a big spider in the house. But the fear was gone!
I had a feeling I would find her that night once all the lights were out. Sure enough, after lights-out I had a look with a torch and found her on the pantry wall. I put a glass jar over her, slid some card behind that, took her outside, and released her.
She did me proud and in a significant way changed my life because my spider phobia had gone and has never returned. I hope I was a good host. I now go out of my way to be ultra-nice to spiders (aah, so that's why you don't vacuum up cobwebs says the wife); trying to make up for those I killed in my other life.
A psychologist writes:
"This is an instance of 'flooding'. The client is subjected to so much of the threatening stimulus that their fear response is extinguished. This contrasts with their usual behaviour, which is avoidance. When you avoid the threatening stimulus, you feel relief. That simply reinforces the avoidance and so perpetuates the phobia.
This was backed up by desensitisation. In effect you approach the threat from a distance (sometimes first imagining it before you even have to see it, let alone touch it). As you learn to manage each stage, i.e. without excessive fear, you move to the next. "
But central to defeating a phobia is to live through exposure to the threat. Sure, you feel your heart is going to burst out of your chest - but guess what? It won't. And when your panic has run its course and the dog turd / spider / snake / you name it is still there, it's like "What else is left?" That works, avoidance doesn't.
And it is so nice not to experience that horrible lurch in the stomach any more. And so nice not to have to kill innocent spiders.