To be motivated by Good in destroying evil is good, but motivation merely to destroy Evil is itself evil

People like to believe that it is A Good Thing to destroy evil; but this is only true when the motivation to destroy evil is positive. 

That is, when the motivation to destroy evil is Good. 

(As your mother told you: Two wrongs don't make a right! - they really don't.)

If some-thing evil is eliminated - but there is not a motivating Good reason for doing it; then there will be a bad motivation; and there will be net harm in the world.

(One way or another.)

You cannot get good out of evil intent; and the desire for destruction as such, on its own is an evil.

Only when the desire for destruction is a means to the end of Good (that is, in harmony with God's creative intent) can destruction be justified. 

Consider the example of hatred of some evil thing - lets say an evil organization or government or dictator. Something really evil. 

It is right to hate evil - therefore (surely? one might assume) it would be A Good Thing to destroy it?

But not necessarily so. 

There are (think about it...) many, many examples from history when an evil institution or person has been destroyed - by revolution, conquest, assassination -  and what came after was worse. Sometimes much worse. 

Indeed, this is usual. 

The reason that such outcomes are usual is that Good motivations - and I mean real Good motivations - not pretend Good motivations that are just disguises for resentment or malice - are rare. 

I think you would find that good outcomes from destruction occur only when the destruction is a means to a genuinely Good end. 

This is important because nowadays there are - at least so I believe - no genuinely Good motivations in public discourse or politics in the West. 

I mean that none (not one) of the institutions, parties or persons who are engaged in the public realm, and have power to destroy, have genuinely Good motivations. 

Therefore, necessarily, destroying things in The West will turn-out badly, one way or another... 

(There are many, many such possibilities for how things will - whether predictably or not - go wrong.) 

This is yet another example of: Be careful what you wish for!