Of course it is very fashionable to smite your forehead and mutter that education ain't what it used to be but, if you are providing training material, there are two problems with the concept of trying to offer a proof of every statement you make. The first is that the proofs often become so complex that they obscure the simple idea you are trying to get across, the second is that what we often regard as 'truths' on inspection turn out only to be approximations that hold good in certain sets of circumstances.
Our policy is to avoid complex explanations when they are not required by the syllabus, but always be ready to justify a statement with a full proof if a student is interested. As GB might have said, I agree with Keith.