You propose an argument, only to have someone misinterpret and bastardize it, then argue against a point you never made in the first place. This is the classic straw man argument.

In another scenario someone makes a claim and you successfully refute it. Instead of accepting the refutation, they simply change the criteria, their position, or their requirements for evidence. This is an example of moving the goalpost.

Now let's combine them. You propose an argument only to have someone misinterpret and bastardize it, then argue a point you never made in the first place. You correct the misunderstanding, but they simply create a new, equally bastardized version of your argument and proceed to argue against it. This is moving the straw man.

Moving the Goalpost: http://en.wikipedia.org/wiki/Moving_the_goalposts

Straw Man: http://en.wikipedia.org/wiki/Straw_man