Question: Why is it that whenever witnesses are required in Islam, two women are required to take the place of only one man?

The Quran in Sura 2:282 says:

> 
> And let two men from among you bear witness to all such documents
>  [contracts of loans without interest]. But if two men be not
>  available, there should be one man and two women to bear witness so
>  that if one of the women forgets (anything), the other may remind her.
> 
> 
>

Answer: 
Quran itself states the reason clearly: "if one of the women forgets (anything), the other may remind her". This is about the way human mind works. Men keep the event in more details. This is about nature and something like a man being physically stronger than a woman. Allah that created human knows it better than any authority. So Quran have to be obeyed and a Muslim should not put questions on words of Allah. Interpretation of all cases is not so simple. We can not disobey a command while we could not find a reason for it.
I think this area is heavily disputed (on witnesses in general). While the Qu'arn is very clear in your example, it does not explicitly extend that beyond financial matters.

The most commonly accepted reason that I have seen is that financial matters are generally not in the women's sphere of expertise or interests. On the contrary, many scholars say that a woman's testimony alone is fine on matters that deal with womanly areas, such as child birth. The number of women can be different depending on the scholar though.

Also, as a wrench in the system, in cases where a husband accuses his wife of unchastity, her testimony will invalidate his.