Why do impurities lower the melting point of an isolated substance?
It's a very general statement, but it's not always true. I'll explain why it's often true, and give a counter-example at the end.



Your majority component B and the impurity (let's call it A) form a binary system. In most cases, such binary mixtures exhibit a solid–liquid phase diagram as follows:



(image taken from these lecture notes).

This binary phase diagram has pure A on the left, pure B on the right. A and B form, somewhere, a eutectic. It is the point here at concentration e and temperature y. Because the existence of a eutectic point is guaranteed for any A/B binary system, and because the eutectic corresponds to a lower temperature, your liquidus curve decreases with increasing impurity concentration, and the impurity thus lowers the melting point.

However, not all binary mixtures form a eutectic. In the words of Wikipedia:


  Not all binary alloys have a eutectic point; for example, in the silver-gold system the melt temperature (liquidus) and freeze temperature (solidus) both increase monotonically as the mix changes from pure silver to pure gold.


The corresponding phase diagram is as follows: