We will focus on the word translated as "right." The King James Version reads "power." This is exousia (Strong's #1849), which has a variety of usages: "power," "authority," "capability," "ability," "strength," "entrusted," "commissioned." It implies the liberty or power to do something. This Greek word has its roots in exesti. The two of them, exesti and exousia, combine two different ideas, "right" and "might." A person can be given the right to do something and then given the might or power to do it. What does God do here through Jesus Christ? As many as receive Him, to them He gives the right and the power to become children of God.
John W. Ritenbaugh
Faith (Part 5)
Just because we see does not mean that we will believe because there is a spiritual aspect to this sort of seeing and believing. This passage indicates that "His own" showed not even a flash of recognition as to His true identity.
Consider the incongruity of this. We frequently hear of personalities in the public eye affecting some kind of a mode of dress or lifestyle that will set them apart and make them instantly recognizable. In this regard, compare Jesus Christ, the most unique Personality that ever lived in the history of mankind! He was a one-of-a-kind, the only human who ever lived life sinlessly. Yet, even those of His generation who saw Him could not identify Him, God in the flesh!
This suggests that one must be predisposed to believe, to have the ability to "see." It is interesting to note that, to those who exercised this faith, "He gave the power [right, authority, ability] to become the children of God" (verse 12). Only those who "see" and then "receive" Christ can enter into a relationship with God that results in nothing less than the creation of a new being.
John W. Ritenbaugh
Do You See God? (Part One)
Other Forerunner Commentary entries containing John 1:12: