"Tiger girl Yan can marry a dog" This is the line in the "Romance of the Three Kingdoms" that Guan Yu rejects Sun Quan's request for marriage, and the real history does record that Yu refused Sun Quan to marry Guan Yu's daughter for his son:
First, Quan sent the envoy as a daughter of Zi Suo Yu, who insulted and insulted his envoy, and was not allowed to marry, and Quan was furious. - "Romance of the Three Kingdoms: The Biography of Guan Zhang Ma Huang Zhao"

Translated, it means that before Sun Quan betrayed Guan Yu in 219 AD, Sun Quan once sent emissaries to ask his son to marry Guan Yu's daughter, but Guan Yu insulted Sun Quan's emissaries and refused the request for marriage, and Sun Quan was furious. Guan Yu's refusal to marry and various factors eventually led to Sun Quan and Lü Meng attacking Guan Yu and capturing Jingzhou. Then there is a question, why did Guan Yu refuse to marry Sun Quan?
Because there is no record of the reason in the history books, there has always been a lot of speculation, some people say that Sun Quan is making things worse, because Sun Quan married Guan Yu in order to win Guan Yu and split the relationship between Guan Yu and Liu Bei; some people say that Guan Yu is arrogant and looks down on Sun Quan; others say that Guan Yu does not marry his daughter to Sun Quan because he wants to marry his daughter to Liu Chan (this I think is too unreliable).
I have always wondered why Guan Yu would reject Sun Quan and insult Sun Quan's emissaries, but recently I have been thinking hard and seem to have found some clues and communicated with everyone.
Mrs. Sun's lessons
Since the Battle of Chibi in 208 AD, Liu Bei's clique finally had the four counties of Jingzhou as a base, in 211 AD Liu Bei entered Shu, Guan Yu and Zhuge Liang stayed in Jingzhou, in 214 AD the War in Yizhou was glued, Liu Bei urgently summoned Zhuge Liang, Zhang Fei, and Zhao Yunchi to aid Yizhou, and since then only Guan Yu himself has remained in Jingzhou, until 219 AD, when The military and political affairs of Jingzhou were the responsibility of Guan Yu.
Therefore, Sun Quan proposed to Guan Yu that the time of marriage should be between 214 AD and 219 AD. Sun Quan was a qualified politician, so the means of marriage were used very skillfully, and in 209 AD, Liu Bei led Jingzhou Mu, and the momentum was greatly enhanced, and Sun Quan married his sister to Liu Bei in order to consolidate his relationship with Liu Bei (Quan was slightly afraid of it, and entered the sister to be good).
However, the political marriage between Lady Sun and Liu Bei was not as happy as in the "Romance of the Three Kingdoms", Lady Sun was quick in intelligence and strong and brave, with the style of her brothers of the same sect, and more than a hundred servants around her, all of whom guarded her with swords. Even characters such as Liu Bei, every time they enter the inner chamber, they feel afraid and afraid in their hearts, and the two are basically wary of each other, where there is any feeling to speak of.
In the sixteenth year of Jian'an (211 AD), Liu Bei entered Shu, so Sun Quan sent a large ship to welcome her sister back to Wu, and Lady Sun planned to take Liu Chan with her, but fortunately Zhuge Liang promptly sent the Yamen generals Zhao Yun and Zhang Fei to intercept liu chan together on the river, and Fang recaptured Liu Chan, and she never returned, and there was no news. Three years later (214 AD), after Liu Bei dédicated Yizhou, he officially remarried Wu Yi's sister as the main chamber, and the deeds since then are unknown.
The marriage between Liu Bei and Lady Sun was a failure, lasting only two or three years, and the tragedy was basically caused by Sun Quan (the marriage was also given to Sun Quan, and the return to Eastern Wu was also taken by Sun Quan). With such a lesson from the past, how could Guan Yu agree to marry Sun Quan?
The question of the age of Sun Quan's son
Another detail that is easy to overlook is the age of Sun Quan's son. Sun Quan had seven sons in his lifetime, the eldest Son Deng was born in 209 AD, the second son Was born in 213 AD, and the other five sons were born after Guan Yu's death. Even according to the oldest Sun Deng, by the year Guan Yu was killed in 219 AD, Sun Deng was only 10 years old.
Even if the ancients married early, they would not get married at the age of 10, and in the sixth year of the Huang Dynasty (225) in history, Sun Quan married Zhou Yu's daughter to the crown princess (Sun Deng was 16 years old) for Sun Dengjuan. Therefore, after seeing Sun Deng's age, I even doubted whether there was a problem with the record in the Romance of the Three Kingdoms, even if Sun Quan just wanted to make a marriage contract with Guan Yu and marry when the children grew up, it was a bit unreliable.
Therefore, considering the two reasons for the failed marriage between Lady Sun and Liu Bei and the young age of Sun Quan's son, it is estimated that in Guan Yu's view, Sun Quan's request for marriage is basically nonsense, so Guan Yu will refuse, and insult Sun Quan's emissaries in anger. Of course, the above is only a personal opinion, welcome to criticize and correct in the comment area!
References: Notes on Pei Songzhi in romance of the Three Kingdoms, And Lu Simian in History of the Three Kingdoms