The Festival of Shelters or Tabernacles falls at the end of September and every adult male Jew who lived within fifteen miles of Jerusalem was LEGALLY bound to attend it. Also, there would have been many Jews from further afield who would make the journey to attend. It lasted for eight days. In this passage Jesus is revealed as having a very powerful sense of timing. It would have been easier for Him to accompany His brothers and disciples to the Feast, but He choose to go a bit later and secretly. ''My time is not yet come'' was a phrase He used frequently: read 2 v 4, 7 v 30, 8 v 20 and 12 v 27 for examples of this. However, what appears to be an identical reply from Jesus as say, His response to His mother at the wedding in Cana, is actually a different word in the original. Here the word Jesus uses means an opportunity, the psychologically best time. He delayed His appearance until the crowds were at their largest. One of His reasons would have been that He brought out the strongest feelings in people- expectation, longing, love, derision and hatred.
I always have the feeling in reading through the Gospels that Jesus was aiming His addresses at those with listening and open ears; He wasn't that bothered about those He reacted scornfully. Remember that in His parable of the Sower, a parable that gives clues as to why Jesus did and said what He did, Jesus spoke about the good soil representing 'honest, good-hearted people who hear God's Word, cling to it and patiently produce a huge harvest'. As we know the great majority of the Jewish religious leaders hated Him, but a few like Nicodemus were listening and responding in their hearts. These are the ones to whom Jesus was speaking.
Be honest with yourself: are you amongst the 'honest, good hearted people'? Do you have too much to hide or are you willing to open up yourself to the all-seeing, yet merciful and forgiving gaze of Jesus?