One.
In 220 AD, after Cao Cao's death, Cao Pi succeeded to the throne of Wei, forcing Liu Xie, Emperor Xian of Han, to abdicate, ending the history of the Eastern Han Dynasty. After Cao Pi ascended the throne and became emperor, he posthumously honored Cao Cao as Emperor Wu of Wei, and the temple name was Taizu. In the same year, Sun Quan proclaimed himself emperor and posthumously honored Sun Jian as Emperor Wulie, the ancestor of the temple name. However, after Liu Bei became emperor in 221 AD, he did not posthumously respect his father, why?
For Cao Pi, Cao Cao paved the way for Wei, eliminated many princes, and created the conditions for his smooth succession to the dynasty. Sun Jian killed the generals in the crusade against Dong Zhuo, leaving an important foundation, so Cao Pi and Sun Quan needed to respect their father after the emperor.
However, Liu Bei started from scratch and successively attached himself to many princes, suffering frequent setbacks. Although he relied on his own efforts to establish Shu Han after the Battle of Chibi, his father did not contribute to his cause. For Liu Bei, there is no need to respect his father, and there is no doubt about it.
Two. Liu Bei worked hard to take Jingzhou and Yizhou, and established Shu Han. However, because Guan Yu was killed by Eastern Wu, Liu Bei failed to launch the war and finally died of illness. Shu Han was built by Liu Bei, so he did not honor his father. In the name of Kuangfu Han Dynasty, Liu Bei established the Shu Han Dynasty to continue the Han Dynasty. Liu Xiu's pursuit of his father was opposed, and Liu Bei may not be able to build his father's temple.
During the Ming Dynasty, Jiajing faced the problem of his father's honorific title after ascending the throne, and similar ceremonial disputes also occurred in history.
Three. 
Although Liu Bei was not the son of Emperor Yuan of the Han Dynasty, in order to inherit the orthodox status of the Han Dynasty, he could only become the son of Emperor Yuan of the Han Dynasty in terms of etiquette. Liu Bei established Shu Han and was unable to build a temple for his biological father, similar to Liu Xiu's situation. Liu Bei faced the threat of being attacked by the separatist side, Eastern Wu and Cao Wei, and failed to pay attention to the issue of posthumously honoring his father.
Summary. 
Liu Bei did not honor his father for many reasons, including his father's failure to contribute to the establishment of the Shu Han Dynasty, the self-construction of the Shu Han Dynasty, and the tradition of etiquette and law. Unlike Cao Pi and Sun Quan, Liu Bei faced a complex situation and paid more attention to the stability of the dynasty, so that he did not focus on honoring his father.
The above is a detailed analysis of the reasons why Liu Bei did not honor his father after establishing Shu Han, as well as the differences with Cao Pi and Sun Quan. This question involves many aspects such as history, politics and culture, and it is thought-provoking.
First of all, the article points out that Liu Bei's father did not contribute to the establishment of Shu Han, which is very different from the situation of Cao Pi and Sun Quan. This involves the evaluation criteria of historical contributions to the figures, as well as the trade-offs in the posthumous pursuit of titles. Cao Pi's father, Cao Cao, played an important role in unifying the north and creating the conditions for him to rule, while Sun Jian also showed great military talent in his crusade against Dong Zhuo. In contrast, Liu Bei's father does not seem to have left a significant footprint in the founding of Shu Han, which may be one of the reasons why he was not posthumously honored.
Secondly, Liu Bei started from scratch throughout the process, experienced many twists and turns, and relied on other princes many times. This underscores Liu Bei's ups and downs in history, as well as his perseverance in building the Shu Han dynasty through his tireless efforts. Although he did not honor his father, Liu Bei's personal struggle history became a footnote to history, which also made the establishment of Shu Han even more hard-won.
On the other hand, the text also mentions that Liu Bei upheld the banner of Kuangfu Han for the establishment of Shu Han. This highlights Liu Bei's sense of responsibility for historical inheritance, and at the same time, he cannot ignore his connection with the Han family. Perhaps it was based on this sense of responsibility that Liu Bei chose not to honor his biological father in order to better serve the entire Han family.
The article also briefly mentions the "Great Rites Debate" that took place during the Ming Dynasty, a historical event that contrasts the attitudes of different emperors on the issue of their father's honorific title. This provides readers with a historical reference, makes Liu Bei's decision more unique, and also confirms the analysis in the article.
In general, Liu Bei's decision not to honor his father was the result of a combination of factors, including not only from the perspective of historical evaluation, but also involving Liu Bei's personal political wisdom and sense of responsibility. Such historical issues have triggered people's in-depth thinking about the values of respecting relatives and filial sons, respecting kings and defending the country.
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