I read this example
Flying high above the trees, the butterfly was impossible to catch
I thought that the sentence must have been made like this:
Flying.....,the butterfly was impossible to be caught.
Which one of those is correct?
The first example is correct as it is:
The butterfly was impossible to catch.
This construction is an example of "tough movement", as explained here:
Wikipedia "Tough movement"
In formal syntax, tough movement refers to sentences in which the syntactic subject of the main verb is logically the object of an embedded non-finite verb. The following sentences illustrate tough movement.
- This problem is tough to solve.
- Chris is easy to please.
So, in your example, butterfly is the subject of is, and it is also logically the object of to catch.
(The word "tough" is used to describe the grammar phenomenon because, like "impossible" in your example, it's one of a class of words that can be used in that construction. The linked article has a list of such words.)