Homosexuality

"Rational: endowed with the faculty of reason."
"Reason: a basis or cause, as for some belief, action, fact, event, etc."

Actually yes the actions of the rabid dog are rational for there is a reason as to why it did what it did. The chemical reactions inside of the dog's brain caused it to maul the child, thus there is reason behind the mauling, therefore it is rational. Although it might not be right it is still rational.

I shall say it again, although we might not comprehend why something happened does not make it void of reason. Everything has a reason for occurring for if it didn't, it would not have occurred.

You're trying to cover up a faulty argument by assigning false definitions to terms in your examples. Here is your original argument, with the noteworthy portions bolded:

Everything is rational outside of the world of mathematics. Everything has a reason as to how and why it occurred/existed. If there was no reason as to how or why, said action/object would never have occurred/existed. Although the human mind may not be able to comprehend as to why/how something occurs/exists does not make it void of reason. Therefore, since it exists/occurs, it is rational.

As to find out the reason why/how, go study the mind and how it works.

While everything has a reason behind it, it may not necessarily be rational. Rational is driven by logic. A spree killer shooting up a school is not driven by logic, nor is a rabid dog.