How is it pretentious? I feel the same way. When people ask me what programming is like, I tell them it is 50% understanding the business problem, 49% problem solving, and 1% writing code.
Because first, it's trite: literally every person in the organization is hired to "solve business problems". Second, I think it's pompous to elevate one's position to some sort of strategic "problem solver" role when, unless you are a consultant, you are hired to translate requirements into working software systems. Your boss would roll her eyes at the "I solve business problems" language. She would say, "Uh-huh. You do that - solve the business's problems. Just make sure you close your Jira tickets while you're doing it."
"translate requirements into working software systems" demonstrates fundamental misunderstanding what programmers do. It is a decades old and rather common misconception. It is why there is "mythical" in the Mythical man-month book (1975).