Why did Joseph plan to quietly end his engagement to Mary after learning she was pregnant?
Joseph, being a just man, was unwilling to make Mary a public example after she was found with child before the marriage was consummated. Therefore he planned to put her away privately, keeping the whole matter secret rather than exposing her publicly.
Les explains that Mary was espoused to Joseph before they came together, meaning before their marriage had been consummated, and she was found with child of the Holy Spirit. Joseph, her husband, being a just man and not willing to make her a public example, was minded to put her away privately—in other words, to keep the whole thing secret. The context later shows the angel of the Lord appearing to him in a dream, telling him not to fear to take Mary as his wife, because what was conceived in her is of the Holy Spirit.
Then Joseph her husband, being a just man, and not willing to make her a publick example, was minded to put her away privily.