So far in the series, it's not explained why Nezuko is the only one that was turned into a demon, but chapter 196 of the manga does give some insight into what happened when Kibutsuji attacked the Kamado family.
So from this you can determine that:
Kibutsuji doesn't necessarily pick Nezuko to turn into a demon. He was trying to make a demon that could conquer the sun and appears to try with every member of the family. All family members were assumed dead, Kibutsuji comments on it not being easy, and only later does Tanjiro show up to save Nezuko and find out she's a demon. In other situations, like when Kibutsuji turns the man into a demon when he first meets Tanjiro, the process happens immediately. The best information as currently available in the manga points to Kibutsuji trying with the entire family, assuming he failed, and moving on only to later find that Nezuko was "alive."
Will update if new information becomes available in later chapters.