I wonder whether the spiders held an Arachnid Therapy Session to get over the trauma of being repeatedly caught and released 40 times in a day?
Yes, there's an instinctive reaction to them. It's a reaction because in other parts of the world, they can be a problem - but even there, it's not particularly useful to be shrieking and thundering around to escape, as doing that could result on you standing on a snake, alerting a Jaguar or otherwise getting yourself hurt.
Learning to catch them unharmed is vital - however, if you're so over reactive to them that a photo is too much, perhaps drawing cartoon ones could be a useful step in making them friendly? Then you could make them out of scraps of pastry or, if you have kids, playdo? Pipe cleaners and a screwed up ball of paper can result in incredibly cute ones that even work on real spiders - as you'll see if you dangle it near; they're so large that our usual spiders will immediately try their hardest to run away.
Once you can handle a model one you've made (and possibly had a few ARRGH moments from seeing it on the coffee table before realising it's your model one with googly eyes), I don't think it's too daft to practice catching your model with a glass and card.
Then you're primed to be able to do it with a real one. Put the glass down and try to look at your prisoner. Notice their colours, the intricacy of detail. If need be, get somebody else to do the release outside, but if not, just remember that it's OK to put the glass down, then lift/tilt the glass away from you and step away.
Before long, you'll be telling others to leave them alone and will be rescuing them from the scariest creature of all - humans.