I did not know him, but the reason why I came baptizing with water was that he might be made known to Israel.... I did not know him, but the one who sent me to baptize with water told me, "On whomever you see the Spirit come down and remain, he is the one who will baptize with the holy Spirit" (1:31, 33; all quotations come from the NAB, unless otherwise indicated).
This would seem to contradict the claims of St. Luke's gospel that Jesus and John the Baptist were kinsmen whose mothers spent several months together. Moreover, we know that Jesus' family visited Jerusalem for the pilgrimage festivals when He was growing up, so it seems unlikely that His kinsman John would not have known Him. What are we to make of this seeming contradiction?
The answer, I think, lies written all over the chapter, and tells us about a lot more than simply solving a small textual problem. So let's go to the beginning of the gospel. There St. John takes us all the way to beginning of time, back to Genesis, opening with the same line, "In the beginning..." (1:1). We are told that "the light shines in the darkness / and the darkness has not overcome it" (1:5). The NIV says that "the darkness has not understood it." Does that ring a bell with Genesis? "The woman saw that the tree [of knowledge of good and evil] was good for food, pleasing to the eyes, and desirable for gaining wisdom. So she took some of its fruit" (3:6). Seeking knowledge, she grasped after what had not been given, bringing death upon the human race. So too the darkness in St. John's gospel grasps, but it comes up short. It can neither understand nor contain the light. But "the true light, which enlightens everyone, was coming into the world" (1:9). Notice who does the action: enlightenment is received by those who have it; it is not something they produce or achieve for themselves.
Returning then to the enigmatic figure of John the Baptist: when asked if he is the Messiah, Elijah or the Prophet, he denies that he is any of them. When he sees Jesus he quickly announces, "Behold the Lamb of God!" (1:29). John is keen to avoid the limelight. And I think his comments about knowledge - or rather, ignorance - of Jesus and His identity underline this. John did not grasp at an understanding of who Jesus was. He did not ascertain it by his own powers of mind. Rather, it was revealed to him by God, something for which he could take no credit.
This theme of knowing infuses the entire chapter. Those who think they can know by their own power fail - "the world did not know him... his own people did not accept him" (1:10-11). But to those who come before Him in humility of heart, Jesus says, "Come, and you will see" (1:39). For those who accept that knowledge is an invitation and a gift, Jesus promises "you will see the sky opened and the angels of God ascending and descending on the Son of Man" (1:51). Not that we could ever see such things on our own, but God, in His self gift, reveals them to us.