People with irrational fears should be aware that they're irrational. If you treat an irrational fear as if it is rational, then you only encourage and reinforce the fear. People can recover and move past phobias, but it doesn't happen by being coddled.
Actually, that is a lot easier said than done. People with irrational phobias know that they are irrational--but it is beyond their control. I would know, as I am one of those people. Seeing a spider in my home can put me into a frightful attack of fear, and while in the midst of my crying and hyperventilating, I am well aware that it is ridiculous--but I really cannot help it. I have to get my husband or someone else to kill the little creature for me, or I can't go on with my day.
Phobias, while irrational, are a real thing to those who have them, and it is very hard to overcome a phobia. So, if you are lucky not to have one, at least have the decency to be sympathetic and not judge those of us who have phobias as if we are incompetent morons.
That said, I still don't think it's logical to remove spiders just because some of us are terrified of them.