Happy Easter and Happy Birthday Jesus!
April 16 or 17 is the day that Ptolmeic Astrologers calculate to be the birthdate of Jesus of Nazareth as it would have attracted the Astrologers from the East also known as the Magi, who followed what was called the Star of Bethlem but was really the astrological configuration proper for the birth of the King of the Jews. Serveral explations of the calculation are available. A good one is https://www.thenakedscientists.com/forum/index.php?topic=69233.0 .
So why did it not stay there? I suspect that the early Church put no faith in astrology. Additionally, Jesus birthday was commemorated on the Winter Solstice, which before adjusting for the progression of the Equinoxes, was December 25th. This date was Saturnalia (a great party with amble debauchery and drunkenness) and the attempt was made to make it more pious, with Jesus being recognized as the light of the world just as Chanukah is placed in the same time period.
There is another more important reason, which the coincidence of Easter and the true birthday reveal. In early Christianity there were those who were willing to equate resurrection with reincarnation. Having the date of the Easter and Jesus’s birthday closely coincide would reinforce that link and cut short the Easter season. Moving the Nativity feast to June would decrowd the calender, but it still sends a reincaration message the Church fears. Too bad for them. Happy Easter and Happy Birthday Jesus!