Well, we might start with how Wilhelm and Theresia(his wife) got married 40 years ago. It is already popular story in-universe as 'Love song of the Sword Demon', about love story between Wilhelm Trias and Therasia Astrea (Van is a title only addressed to worthy member of family).
Wilhelm Trias was born under the noble family but didn't have any succession right. So, he entered the army seeking future and promoted fast enough with his combat sense in Demihuman War(It was more like a rebellion than actual war).
Someday, Wilhelm met a girl in ruin who was seeding flowers. When the girl asked him why he is wielding a sword, he replied "Becuase I don't have any other way." They met often and when Wilhelm fall in love with her, his reply changed into "Because I don't know any other way to protect."
When his family's hometown was attacked by rebel force, Wilhelm went there but couldn't stop massacre on his family and villagers. Just before Wilhelm was about to die along, the Sword Saint, a girl he met before, comes and saves the day (Wilhelm didn't know her first name). Wilhelm became furious that she hid her status as Sword Saint, attacked her and promptly curb-stomped by her. She repeated his line, 'Because I don't know any other way to protect' and leaves, when Wilhelm promised himself he will take that responsibility back.
Therasia Astrea was born with Blessing of Reaper, and any wound inflicted by her could be fetal. Because of that, she hated sword and Astrea Family didn't train her swordsmanship either. It all changed when she succeeded the Blessing of Sword Saint in age 12. She finally agreed on joining the Demihuman War to protect Wilhelm.
With the Sword Saint's power and De Facto leader of the rebellion, Valga Cromwell presumed killed by Wilhelm in an assault on Lugunica Palace(Explains how he popped up from the floor in episode 13), Demihuman War was swiftly over with Lugnica victory. In a triumphal celebration, Wilhelm abruptly enters and issues a duel against Therasia. When she lost, Wilhelm proposes her claiming "You no longer have to wield the sword because you're weaker than me" which Therasia answered yes with crying.
However, the song ends in tragedy when their son, Heinkel was ordered to lead the White Whale hunt. Therasia took his position instead, and prevented Wilhelm from coming along by inflicting a wound (He already had other mission: finding a missing daughter of royalty)
Therasia's hunting party was completely annihilated, and from then Wilhelm spent everything on revenge, abandoning Astrea family and entering Crusch's side because she was the only noble agreed to help him with hunting White Whale.
To summarize the aftermath, Therasia's death almost broke the family apart, and her 2nd death really broke the family apartin Arc 5
Wilhelm hates both his son(Heinkel) and grandson(Reinhard), because they all took part in Therasia's death. She went there because Heinkel refused to do so, and Reinhard took away her Blessing of Sword Saint while she was fighting, greatly decreasing her capability.
Heinkel(Almost like fantasy-born Subaru) also has reasons to hate both his father(Wilhelm) and son(Reinhard). Wilhelm abandoned the family for revenge, and Reinhard beat him in a duel when he was only 5 year old, denying every effort he spent on swordsmanship (It was mentioned almost joke-like in Author's Q&A, but tragic in his sight).
We never saw what Reinhard really thought about this.
