Where did variable = null as "object destroying" come from?

It's FUDcargo cult programming (thanks to Daniel Earwicker) by developers who are used to "free" resources, bad GC implementations and bad API.

Some GCs didn't cope well with circular references. To get rid of them, you had to break the cycle "somewhere". Where? Well, if in doubt, then everywhere. Do that for a year and it's moved into your fingertips.

Also setting the field to null gives you the idea of "doing something" because as developers, we always fear "to forget something".

Lastly, we have APIs which must be closed explicitly because there is no real language support to say "close this when I'm done with it" and let the computer figure it out just like with GC. So you have an API where you have to call cleanup code and API where you don't. This sucks and encourages patterns like the above.

It is possible that it came from VB which used a reference counting strategy for memory management and object lifetime. Setting a reference to Nothing (equivalent to null) would decrement the reference count. Once that count became zero then the object was destroyed synchronously. The count would be decremented automatically upon leaving the scope of a method so even in VB this technique was mostly useless, however there were special situations where you would want to greedily destroy an object as illustrated by the following code.

Public Sub Main()
  Dim big As Variant
  Set big = GetReallyBigObject()
  Call big.DoSomething
  Set big = Nothing
  Call TimeConsumingOperation
  Call ConsumeMoreMemory
End Sub

In the above code the object referenced by big would have lingered until the end without the call to Set big = Nothing. That may be undesirable if the other stuff in the method was a time consuming operation or generated more memory pressure.