Why did Arjuna rejected the Urvashi (उर्वशी ) ?
Arjuna considered Urvashi (उर्वशी ) as his mother, this is because in Treta Yuga, King Pururava and Urvashi were married and they was ancestor of the Pururavas, from whom descended the Yadavas, Kauravas and Pandavas.
This is mentioned by Arjuna himself in the Mahabharata Vana Parava chapter 46 verse 46-47
यथा कुन्ती च माद्री च शची चैव समा इह।
तथा च वंशजननी त्वं हि मेऽद्य गरीयसी ।।
In my eyes you are similar to Kunti, Madri and Sachi. Since from you the Puru Lineage started, so you are respectful to me like a Guru.
गच्छ मूर्ध्ना प्रपन्नोस्मि पादौ ते वरवर्णिनि।
त्वं हि मे मातृवत्पूज्या रक्ष्योऽहं पुत्रवत्त्वया ।
I respect you by keeping my head on your feet, you please go away. You are like a mother in my eyes and you should also protect me like your child.