Dirty Dishcloth.

There are some things that defy understanding, standing at the sink washing up the breakfast things I notice one of them. How come that the dishcloth, that is less than a week old, looks grubby already.

It started life all white and fresh but in 4 days it has become off white and in need of bleaching. The troubling thing, for me at least, is that the dish cloth is in hot detergent water for most of its working life, being plunged and squeezed and generally agitates in a detergent that is specifically designed to shift grease and dirt from all manner of pots and pans.

I checked the content of the washing up liquid it its main cleaning agent is something called "non-ionic surfactants" which seems to be the exact same thing that makes up washing machine liquid. So the question is, how does a dish cloth get dirty washing about in the same cleaning stuff that gets clothes clean in the washer.
I suspect is connected with my next dilemma- Why do dishwashers need cleaning.

Every time a dishwasher is in use you put in it the latest wonder agent that will wash cleaner than anyone ever believes is possible. Yet as the plates get cleaned the machine gets dirty. How do they make a cleaning substance that knows it is only to clean the pots and pans and leave the dishwasher greasy?
No, really, how do they? As I said its the same thing that makes the dishcloth dirty.
I didn't say I knew what it was.