One main element is his difficult upbringing in poverty - stricken surroundings. Another is the constant bullying and discrimination he endured due to his physical appearance. And of course, his strong bond with his sister Daki. This bond was what drove him to protect her at all costs and also influenced his actions as a demon. For example, he would go to great lengths to avenge any harm done to her because of their shared experiences of being outcasts in society.
There was a girl and a boy in a competition. It was a race. The boy was overconfident and made some taunting remarks towards the girl before the race. This made the girl determined to win. During the race, the boy tried to block the girl's path a few times. The girl, not one to be bullied, elbowed him gently but firmly out of the way. In the end, the girl won and the boy was left fuming. But the girl just walked away with a proud smile on her face.
Once, I saw a wife and a mistress have an argument in a park. The wife found out about the mistress and confronted her. The mistress tried to act tough at first, but the wife was full of anger and rightful indignation. The wife started shouting about how the mistress was ruining her family. In the end, the mistress, feeling ashamed, ran away.
Tanjiro might use his sense of smell to detect hidden threats. Since his sense of smell is super - enhanced, he could sniff out any demons or traps in the way of saving Rengoku. For example, if there are demons disguised as allies, Tanjiro would be able to tell by their scent.
Gyutaro was born into poverty. He and his sister Daki had a very tough life. They were constantly bullied and looked down upon. Gyutaro had a deformed body which added to his misery. He was filled with hatred towards the world that treated them so badly. In order to protect his sister, he became extremely violent and cruel to those who he thought were threats. His experiences in his early life shaped him into the demon he later became, using his powers to lash out at those he despised.
Jealousy. The wife is jealous of the mistress for stealing her husband's attention and love. And the mistress might be jealous of the wife's legal position in the man's life.
In RWBY fanfiction, the Weiss vs Winter fight can be a display of their different combat styles. Weiss is more about grace and precision with her Glyphs, while Winter, being more experienced, has a more refined and perhaps harsher style. Their fight could also explore their complex relationship as sisters.