Two More Questions from Luke

3. Why did Gabriel pick Zechariah and Elizabeth?
First, Gabriel picked the couple that God instructed him to choose.

Second, both Zechariah and Elizabeth are descendants of Aaron, the first priest of Israel. Only descendants of Levi can be priests, and Aaron was the first descendant of Aaron to be named a priest - this makes Zechariah and Elizabeth special. The role of a priest was to serve as a go between the people and God. The priest was responsible for making the sacrifices of atonement which covered the sins of the people and restored the relationship. John, the announced son of Zechariah and Elizabeth was to serve as a very unique priest - declaring God's mercy and willingness to forgive the sins of all who would repent.

Thirdly, Zechariah and Elizabeth were honest and humble people who were devout in their faith and blameless in their walk before God and their neighbors. They had a heart willing to obey whatever the LORD would instruct them to do, and thus they would be ideal parents for John.

4. How did Elizabeth become pregnant? Was it like Mary or was it through Zechariah?
This is a good question - the text does not make implicit that Zechariah is the father, though the phrasing does make that allusion. With Mary the text makes it quite obvious that the LORD will cause the pregnancy to happen in a miraculous way. What is special about Elizabeth was that her womb was barren in her old age; she had been unable to conceive and now she was beyond the age of being physically able to conceive. The LORD did intervene to make it possible for both Zechariah to impregnate her, as well as touch her womb so that Elizabeth could become pregnant. It was a special birth for which their was much rejoicing.