And dutiful to his parents, and he was not arrogant or disobedient.
After Allah mentioned Yahya's obedience to his Lord and that Allah created him full of mercy, purity and piety, He attached to it his obedience to his parents and his good treatment of them.
Allah mentioned that he refrained from disobeying them in speech, actions, commands and prohibitions. Due to this Allah says,
وَلَمْ يَكُن جَبَّارًا عَصِيًّا
(and he was not arrogant or disobedient).
Then, after mentioning these beautiful characteristics, Allah mentions his reward for this,
وَسَلَمٌ عَلَيْهِ يَوْمَ وُلِدَ وَيَوْمَ يَمُوتُ وَيَوْمَ يُبْعَثُ حَيًّا