All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
First of all, all perfect praise be to Allaah, Who guided you to Islam and we ask Him to make you firm and steadfast on His Religion until the day you meet Him.
As regards your question, Allaah ordered His Slave Nooh (i.e. Noah) to load in the ship two mates (a male and a female) from each kind of animal, and to embark his family –meaning those who believed amongst them –and embark whoever had believed from his people. Allaah Says (what means): {We said, “Load upon it [i.e. the ship] of each [creature] two mates and your family, except those about whom the word [i.e. decree] has preceded, and [include] whoever has believed.”}[Quran 11:40]
However, the son of Nooh was actually not a believer. That is why when he [Nooh] called him to board the ship, he refused; as a result, he was drowned along with other disbelievers. When the deluge was over and the ship rested on Mount Judi, the Prophet Nooh called upon his Lord inquiringly, as in the verse in which Allaah Says (what means): {And Noah called to his Lord and said. My Lord, indeed my son is of my family and indeed Your Promise is true; and You are the most just of judges!”}[Quran 11:45] The expression “My Lord, indeed my son is of my family” means “O my Lord, you have promised me to rescue my family, and Your Promise is the Truth which does not break (i.e. undoubtedly takes place), how is it then that he drowned while You Are the most just of judges?” Thereupon, Allaah Responded to him Saying (what means): {“O Noah, indeed he is not of your family.}[Quran 11:46], meaning that those whom I Promised you to rescue are those who believed amongst your family. It is for this reason that Allaah Says (what means): {...and your family, except those about whom the word [i.e. decree] has preceded.}[Quran 11:40], and the son of Nooh was amongst those whom the Decree has preceded to be amongst the drowned because of his disbelief and disobedience to his father, Nooh . The Saying of Allaah (which means) {Indeed, he is [one whose] work was other than righteous.}[Quran 11:46], means that the work of your son is not righteous (i.e. his deeds are not righteous), worse than this is that he disbelieved in Allaah and hence, he deserved the recompense of the disbelievers.
Therefore, dear brother, you should know that the meaning of the verse {“O Noah, indeed he is not of your family.} is that he is not among those who believed in you or followed you, and he is not among those whom We Promised you to rescue from your family.
Dear brother, the fact that you are guided to Islam, praise be to Allaah, does not mean that your parents are not from your family, indeed they are from your family in regard to family lineage, and Allaah ordered us to be kind and dutiful to our parents even if they are non-Muslims, as clarified in Fatwa 98735. Hence, you should be keen on being kind and dutiful to them, and call them to Islam as you may be a reason for saving them from Hellfire as they were a reason for your existence in this worldly life to worship Allaah Alone.