Four moves for the comp conversation, whether the answer is yes or no, not a general essay on compensation philosophy.
Most first-time managers either overstate their control ("I decided this") or understate it ("it's totally out of my hands") and both versions erode trust. The honest version is usually a mix: their performance rating, where their pay sits inside the band for their role, the market data for that role this cycle, and how much budget the cycle released. Knowing which of those actually moved the needle for this person, specifically, is what lets you give a real answer instead of a shrug.
"I want to be straight with you: I couldn't get you an increase this cycle. Here's specifically why, [the real reason, band position, budget, timing], not a vague one. I know that's not what you wanted to hear. Here's what would change it, and roughly when."
"Why did [coworker] get more" is one of the harder follow-ups, and deflecting it fully ("I can't discuss other people's pay") is technically correct and still lands as evasive. You don't have to share their coworker's number. You can still answer the real question underneath it: what would move this person specifically into a higher band or a bigger increase next cycle. Answer that part directly.