I'm not convinced that there is such a thing as an irrational fear. We might label them that way, and we might not look into it deeply enough to realise the rationality behind it, but we have been classically conditioned somehow that that thing is scary. With spiders and suchlike, that's often something that's passed from parent to child.
I was thinking about this at the weekend; I was listening to James O'Brian's Mystery Hour podcast while I was cooking and there was the question "Do animals suffer from irrational fears like humans?". The callers that tried to answer were all suitably vague, but it got me thinking about whether there really is a thing as an irrational fear at all. We don't tend to think of animals as having the ability to rationalise in the same way as us, and if that is true, then there can't be such a thing as an irrational fear, because any fear they have must be for a reason. What we can see in a dog is what we would deem to be a disproportionate level of fear to the perceived thread - and we can't argue that the dog perceives a threat if she is showing signs of fearfulness. But the dog is being true and honest; she is behaving in a way that seems entirely rational and proportionate to her.
I have claimed I hold an irrational fear of flying, and I did believe it to be irrational. I am a rational person; I know the (rough) statistics on how safe it is to fly. I know what the noises are as the landing gear raises and lowers. I understand how turbulence works, and how the physics keep the plane in the sky. Knowing these things didn't help me not be afraid, so I labelled it as irrational. Then, one day, I was sat on a plane that had been grounded for two hours with us all on board, and with a frantic Spanish lady next to me, who didn't understand what was going on - French air traffic control (quelle surprise). I was travelling alone, so had no-one to squeeze my hand. What I did have was a book, "Dealing with fears and phobias", which I was making my way through. Strangely, it didn't help me at all directly, but as I was reading it, I had a sudden epiphany that the thing I was afraid of was a lack of control. I didn't know anything about psychology at the time, but looking back, I know that the trigger that had started my fear of flying wasn't anything to do with flying at all; it was a bad relationship I was in, where I felt I lacked control. Again, in hindsight, I realised that my fear became profoundly worse during another turbulent time in my life, where again, I felt a terrible lack of control. Since then, the fear had become so bad that I was afraid of the fearfulness itself; I would feel physically ill simply booking a flight, or even watching planes pass overhead, even if I had no travel planned. It might be disproportionate to someone who is not afraid of flying, and I may never have realised what triggered the fear in the first place, but "irrational"? No, I no longer believe it to be that. And even understanding the trigger that caused it, and knowing that is no longer a part of my life, the classical conditioning has been done, and it's an uphill struggle to change a deep emotional response to a trigger.