While I was building Katakuri as a character, I was extremely split between water bending and fire bending. When I think of a fire bender, I think of someone who has some type of anger (cold or hot) along with being dedicated to those who they care about. I feel like they are extremely dedicated to family and goals and they would do anything to reach goals and protect their families (at any cost). 

When I think of Katakuri, I envision someone who tends to keep a "face" in public. Someone who appears collected, organized, and ambitious for what they want in life. While he is very goal orientated, I feel like family, friends, and things he cares about are higher than his true goals (depending on the situation). 
Socially, I feel like he is going to be a character that tries his best to look like he is in total control in and out of public (no matter the situation). This might allow for times of frustration when he cannot claim an answer to an issue. I feel like he is going to be a character with cold and stern anger. Maybe a character that is more on the emotionless side of the spectrum when in basic conversations and socialization, though it is a shield to protect his feelings. Though, he will learn over time to loosen up in front of people and allow himself to show how relaxed, playful, and how much he cares for other living things. 

That's the reason I decided to go with Fire bending as his element.