Why is stopping chkdsk bad?

Solution 1:

The chkdsk program repairs corrupt data structures. This commonly requires matching writes -- oversimplifying, one to remove data from the wrong place and one to attach data to the right place. If you shut the power down when one write is committed to the medium but not the other, the data can be left fully detached.

There are simply too many writes with too many dependencies to ensure that the data is consistent at every conceivable point. If you remove power, you are stopping the process at a random point that may or may not be consistent.