Finally, my answer to the question that you have all been searching for. (I have noticed that since I started this blog, many people who find it do so by searching for an answer to that very question.) Now, I'm not a psychologist or anything, so I'm not really trained to answer the question, but I'll give my take on the situation, none the less. So here it goes.
First issue: If someone is asking "why are women irrational?" it is probably safe to assume the person asking is male, so I'll begin there. The real question at hand is "why do men view women as irrational?" I'm sure that not all men do, but for the purpose of this blog post, I'll be working from that assumption.
Second issue: What do you mean by rational/irrational? Not everyone means the same thing when they use the term. I'll give my understanding of the term and go from there. And yes, I know that at least one reader out there will disagree with me, but that is okay, too.
There are two main sources of my understanding of rationality/irrationality.
1) Notes from one of my professors in graduate school:
The four steps of rational action:
a) state an objective
b) look at options
c) evaluate the likelihood of success
d) evaluate the cost of pursuing options
(Rinehart, class notes, Intro. to Int'l Relations, Sept. 8, 2004)
2) Plato's Republic (I couldn't find a complete copy on line to link to but this site has a decent overview of the part I'm talking about).
Plato suggests that there are three parts to the human soul (or three souls) that guide human behavior. These are the rational, the spirited and the appetitive souls. For Plato, the rational soul is the logical decision-making part of human beings, the linked site equates it with the mind or the intellect. The appetitive soul equates to emotions or desires. Plato sees these forces as constantly in conflict with the rational soul. These attributes are often equated with irrational behavior.
So, to bring the two sources together, rationality is using reason and intellect to weigh options on the path to achieving a stated goal. When emotions and desires (often carnal) cloud an individual's ability to think logically and intellectually weigh options, that individual can be understood as acting irrationally. This can include emotions such as jealousy or love and desires like lust or greed. Also included in irrational motivations would be superstition or blind faith. These are beliefs that cannot be verified using empirical data.
Finally, my answer: Both men and women are irrational at times. We allow ourselves to be distracted from our goals by emotions, desires and non-rational motivations. I believe, however, that men are inclined to view women as irrational, and believe themselves to be wholly rational, because they tend to be distracted from rational pursuits by different irrational forces. Men understand the irrational forces that distract them, like jealousy and lust, but they tend not to understand the irrational factors that affect women. (And of course, there is always the hormone issue, but I'm not gonna go there right now.)
I repeat, I am not saying this is true of all men, I'm just addressing the many men who ask that particular question on a regular basis. Stop and think for a minute, "Is everything I do rational?" The answer is, probably not. Don't use the term to label women, try to understand that it affects all of us, just in different ways.
And although I'm not a trained psychiatrist/psychologist, here is a quote from someone who is.