Duan Qirui can be said to be the largest real power faction among the Three Masters of Beiyang. Yuan Shikai and Duan Qirui had many disagreements before he died, but he had to use him.
Before yuan shikai's death, there were a total of 4 people entrusted with his life, Duan Qirui, Wang Shizhen, Zhang Zhenfang, Xu Shichang, and the "prince" Yuan Keding. Before Yuan Lin died, he only uttered two words in his mouth, the law of covenant, new and old. Old Testament law provided that when a president was unable to perform his duties, he should be succeeded by the vice president. Yuan Shikai's own new law stipulates that the successor to the president should be nominated by the current president, written on the list of gold and stone houses, to be taken out after the death of the president, among the three candidates, one person is determined to succeed to the presidency, Yuan Shikai wrote down the names of the three people are Li Yuanhong, Xu Shichang and Duan Qirui. It is said that the name Duan Qirui was originally written as Yuan Keding, but before Yuan Died, he saw that the general trend had gone, and the people rebelled and separated, knowing that after his death, the people could not support his son, so he secretly changed it to Duan Qirui without Yuan Keding.

This is what Xu Shichang said when several big men elected the president after Yuan Shikai's death:
The death of President Yuan Da, the whole country is grieving, but the country cannot be left without a master for a day, otherwise the country will be in chaos. Shi Chang and the late president have been friends for decades, and they have never intended to be famous, but they have the love of Xiangcheng Miao, and they are really afraid to be on the list of gold and gold. Shichang hereby declares to you that Shichang has no intention of taking the presidency. In my humble opinion, Vice President Lai's succession to the presidency could not be more appropriate.
On the contrary, if Duan Qirui is strongly promoted as president, it may cause opposition from other forces within Beiyang, especially Feng Guozhang, which will lead to infighting in Beiyang and trigger civil war. For the sake of the overall interests of Beiyang, Xu Shichang recommended the relatively weak Li Yuanhong to be this puppet.
At that time, the Protectorate Army and the Beiyang Army were still opposed, and the Protectorate Army insisted that vice president Li Yuanhong succeed him in accordance with the Old Testament law. According to the new law, Lai's name is also written in the first place. Although Duan Qirui is a Beiyang orthodox and has monopoly of power, it is difficult to find a legal argument.
In the actual situation, after Yuan Shikai's death, the Beiyang warlords he cultivated also faced the danger of splitting. At this time, if Duan Chu became president, it would actually be detrimental to maintaining the unity of the Beiyang faction, and it would be easy to cause infighting. Li Yuanhong, on the other hand, had a weak personality, known as Li Bodhisattva, and was placed under house arrest in Beijing by Yuan Shikai in the name of vice president, with no real power. If Li Yuanhong became president, because he did not have a Beiyang background, the Beiyang soldiers would immediately regard him as a dissident and be wary of Li. Because he is an outsider, his becoming president is conducive to the unity of Beiyang. Therefore, supporting Li Yuanhong as president is also a means for Duan Qirui to envelop the Beiyang faction around him. Supporting Li Yuanhong as president, the National Protector Army will also agree, and also avoid the Beiyang faction from becoming the target of public criticism, and although Li Yuanhong is relatively prestigious, he does not have any real power, which is convenient for manipulation as a puppet.
Even so, Duan Qirui was also very unwilling in his heart. He was much taller than Li Yuanhong from the end of the Qing Dynasty, and he despised Li from the bottom of his heart. This can be seen in a small matter: after the ministers agreed that Li Lai would take over as president, Duan Qirui asked Zhang Guogan to visit Li Yuanhong together. After entering the living room, Duan Qirui bowed to Li San, and after Li owed the salute, Duan sat down and did not open his mouth, the three of them looked at each other and sat for more than half an hour, before Duan got up and resigned, and Li Yuanhong was confused. This fully shows that Duan had to lift up Li Dang as president, but he had a complicated feeling of disgust and helplessness in his heart about this matter.
Yuan Shikai adopted a presidential system in which the president concentrated great power. After Yuan Shikai's death, Duan Qirui actually adopted a responsible cabinet system, and Duan Qirui, as the premier of the cabinet, had real power. After Li Yuanhong took office, he had no actual strength and no right to decide anything, but could only sign and seal the things that were decided.
Li Yuanhong and Duan Qirui are not compatible, and there are also historical reasons. When Li Yuanhong was the governor of Hubei, Yuan Shikai escorted Li Yuanhong from Hubei to Beijing almost in the form of a kidnapping ticket, and from then on he was placed under house arrest in Beijing and made a political prisoner. After Yuan's death, Duan Qirui went to see Li, but he did not say a word, which was simply humiliating to him. However, he has always believed that he himself lifted Up Li as president, and in fact, if it were not for Duan Qirui coming forward to support Li, the soldiers of the Beiyang Faction would not have been able to support Li as a big position. After Li Yuanhong took over as president, Duan Qirui did not pay attention to him.
Li Duan has been incompatible, and the situation is the same as water and fire. All the things that Duan Xuan advocated, whether it was justified or not, Li would generally oppose it. In the end, feng Guozhang was pushed back, that is, he did not give Duan as president.