Did Jesus deny being good?

The Skeptics ordinarily don't listen to Jesus, but they do listen carefully on this one (version taken from Mark 10:17-18, but Luke reads no different, and Matthew, though reading differently, really doesn't change the "problem"):

And when he was gone forth into the way, there came one running, and kneeled to him, and asked him, Good Master, what shall I do that I may inherit eternal life? And Jesus said unto him, Why callest thou me good? there is none good but one, that is, God.

From this passage the idea is sometimes taken that Jesus is denying his own goodness, and therefore, throwing out any chance of being recognized as part of the Godhead.

The standard explanation is that Jesus is essentially saying to the ruler, "Do you know what you are implying? You say I am good; but only God is good; therefore, you realize that you are identifying me with God?" [Brooks, commentary on Mark, 162] In Jewish thought, God was pre-eminently good, so that the ruler was indeed offering Jesus a compliment usually reserved for God. Since it is quite unlikely that the ruler truly believed that Jesus was identifiable as God the Son, this looks more like an effort by Jesus to make the man think about what he is saying before he blurts it out or engages in indiscriminate flattery.

Confirmation and elucidation of this explanation is found in Malina and Rohrbaugh's Social-Science Commentary on the Synoptic Gospels (123) in which they explain that in an agonistic (honor-shame) culture, a "compliment" like the rich young man's is actually a challenge and an attempt to put Jesus "on the spot" for they are an implicit accusation that one has been trying to rise above others. Jesus' only alternative was indeed to parry the compliment and redirect it to its appropriate subject (unless he wanted to reveal himself directly and fully, in which case, his claim would have been another challenge of honor to others), thus showing himself honorable by diffusing any accusation that would arouse the envy of an opponent.

Thus it is appropriate that Jesus parry the compliment in a way that does not specifically deny his membership in the Godhead (which, as noted, it does not).

In short, there isn't anything here that has Jesus denying goodness, or membership in the Godhead -- just teaching an overenthusiast and/or challenger a lesson.