Why did Jesus' birth and resurrection happen so secretly or were revealed only to a few?

The scriptural evidence argues otherwise.

1. The birth of Jesus was announced by angels to the shepherds who not only visited Him but also talked about their experiences.

2. Before His birth there was the pre-evidence of Zacharias, Elizabeth, and Mary herself from her experience and visit to Elizabeth.

3. The Magi declared their finding to Herod who cross-referenced it with the Jewish scriptures, but tried to eliminate Jesus.

4. His birth was not a secret. Yet it was a mystery of Godliness against the mystery of ungodliness that is also at work in the world.

Resurrection

This was also no secret.

1. The guards knew about the supernatural visitation, the great angel who rolled the stone....

2. The priests also knew about it and tried to protect the guards by fabricating a tale of disciples stealing Jesus' body, which they were not able to prove and neither their persecuting the disciples could force them to change their testimony of what they saw. 

3. Obviously, given #2, the transformation of the disciples from timid to courageous witnesses was not the result of a mere visionary or subjective experience. 

4. There was claim of a larger body of over 500 people who saw Jesus post-resurrection. It wasn't hallucination. It was also not spiritism. Jesus ate with the disciples and Thomas touched His side.

5. Both Jews and non-Jews were aware of this and it was a stumbling block to both.