Targaryens' Biggest Problem? Maybe They're Just Too Soft
Defend the honour, Viserys…or just don't.
The Targaryens tend to see their 'good name' as a reflection of status rather than honour. This may be why they're a little too soft when it comes to insults and slights against them.
In House of the Dragon season 1, Viserys' position was publicly challenged by Boremund Baratheon when he referred to Princess Rhaenys as 'The Queen Who Never Was'. Otto Hightower advised the king to take action, but Viserys waved off the suggestion.
Later in the series, Corlys Velaryon didn't come out to greet Viserys when he arrived in Driftmark. Lord Lyonel was shocked, but once again Viserys brushed aside the affront.
King Viserys was so desperate not to upset the apple cart that he seemed happy to let anything slide. He didn't even take action to stop an unauthorised war in the Stepstones.
Compare the king's reactions to those of other houses in the face of insult and you'll see that these are soft responses that don't fit with Westerosi tradition.
After an impassioned speech about why he should marry Rhaenyra, Willem Blackwood was insulted by Jerrel Bracken. This was a feud that went back many years, and Willem wasn't going to stand for it. He drew his sword in what looked like a battle he couldn't win, but ultimately killed the man who had insulted his family.
Other families have acted similarly in Game of Thrones. Lord Baelish loved nothing more than having a pop at Ned Stark. But when Ned thought Littlefinger was questioning his wife's honour, he grabbed the schemer and brothel owner by the throat.
Similarly, Robb Stark stood up to Lord Umber in a show of strength that had both men defending their honour. After the wolf bit off his fingers, Umber gave in to Robb, who he saw as a strong leader because he was determined and wouldn't allow an oath to be broken.
And let's not forget that it was the Starks who fed Ramsay Bolton to his own wolves.
Then there were the Lannisters. Cersei never forgave Septa Unella for humiliating her in public. Sansa was stripped and beaten at court by Joffrey, who was very much under the influence of his mother's side of the family. And when Littlefinger challenged Cersei by alluding to her relationship with Jaime, he was on his knees with a knife to his throat within seconds.
Defending the family name and refusing to take insults, it seems, is something all Westerosi houses do. Except for the Targaryens.