Nakula and Sahadeva were less significant characters amidst the Pandavas. They were not shown to be too aggressive nor too inquisitive; they were rather duty minded and content to do whatever Yudhishtra ordained them to do. So, we can say, Krishna perhaps discounted them.
Now, we are left with Yudhishtira, Arjuna and Bhima.
Late Swami Chibhavananda (Sri Ramakrishna Tapovanam, Thiruparaithurai) in his book on Bhagavad Gita, at the introductory chapter, gives the reason for Krishna choosing Arjuna for delivering Gita in the following way:
As regards Yudhshitira, we was already a knower of dharma. He was basically satvic, knew pretty well about what is dharma and adharma and he was spiritually quite evolved. He does not really need a sermon.
As regards Bhima, he was thirsting for the war. He was just waiting for the time to plunge headlong into the war. Animal impetuosity was still dominant in him. Such a man was not not fit for receiving the teaching of or practicing any form of yoga.
But Arjuna’s personality stood somewhat in between these two characters. He was more evolved from animal tendencies but not to the level of knowing the higher realms of spirituality and dharma. He is like a normal man where both virtue and vice are intermingled, who has nagging doubts about what is right or dharma and what is wrong or adharma. Thus Arjuna represented the normal man who is fit for receiving the evolved subject of the Yoga for his spiritual betterment.
From another point of View…
An Avatara Purusha, Mahatma or Satguru is interested in the welfare of all, but they would rather exchange pleasantries with you and take care of your needs when your purpose of going to them is just for mundane existential needs. Only when someone genuinely surrenders and seeks sincere guidance and advice from them on the matters of dharma, God or spirituality, they would opt to teach them by donning the role of a guru.
All along, Arjuna had more of a friendly relationship with Krishna; but when he saw the potential destruction the impending war was going to cause by way of annihilating his own blood relations and teachers, he got scared and jittery. It was at that point that he surrendered with humility to Krishna as his guru and sought his guidance. None of the other pandavas were in such a mental turmoil or confusion as Arjuna was. That’s how Krishna took up His Guru bhava to teach Arjuna the Bhagavad Gita.