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: 
Firstly this is only, as the Quran points out, in the area of business contracts. Where if two men are not brought then 1 man and two women. The Quran also points out that this is in regards to the issue of forgetfulness, because the business world isn't the natural place for a women, the women's responsibility lies in taking care of her children and her home, where it is them man's job to go out and work to support the family. Furthermore as already mentioned two women in regards to business contracts, where if a women in an area of her expertise is to give witness then that witness is sufficient.
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.