Jesus is using a Jewish manner of speaking in which hyperbole (exaggeration) is used to emphasize the point being made. Jesus is teaching that we are to prefer no one to him and what he commands. 
 
However, simply to render it as “prefer” in English would not deliver the full impact of what Jesus says. Thus the English translators properly retain the literal meaning of the Greek word miseó, “hate.” For Jesus is not merely asking for some preferred place in the world of loyalties and ideas, He is asking for a radical preference. Jesus is not just part of our life, he IS our life. 
 
The impact of what he is saying is that we must so strongly love and prefer him, that others might think at times that we “hate” them by comparison. 
 
Thus, “hate” here does not mean to despise, condemn or harbor grudges. But it is a call for a radical preference that the use of the simple word “prefer” does not capture. Jesus uses hyperbole as a way of emphasis. We do this a lot in English as well when, for example, we say things like, “There must have been a million people there.” There may not have even been a thousand, but our emphasis is a hyperbole that means there were a LOT of people there.

No, it does not. Angels do reflect God's glory, as do all creatures to some degree. But angels are creatures, distinct from God, they are not a part (or facet) of God. 
 
Some sympathy for the preacher may be in order however. Sometimes analogies go wrong in live preaching. I suspect what Father meant to say was that angels reflect God's glory in different ways. The Seraphim are the "burning ones" before the Throne of God manifesting God's fiery glory and love, the Cherubim manifest God's glory and will toward creation, and so forth. 
 
I rather doubt Father thinks of angels as part of God. I think his analogy slipped or morphed and that by facets he does not mean to imply the angels are of the same substance as God, but rather, that they reflect his glory differently as facets or a gemstone reflect different qualities.