It's the prerogative of a football club to try and get players at the lowest prices and sell them on at the highest prices, particularly when they're not needed in the first team.
It's also the prerogative of a football player to try and play as much as they can at the highest level they can, particularly when they are young players that need to play to develop.
None of that is really the issue here. The club has time and again tried to get good deals, including loans, for our young players, because that is both in the club's best interest and the player's. A young player that thrives at the right club takes a step in a positive direction to a real career, whether at Liverpool or elsewhere. If elsewhere is the answer, Liverpool reaps the benefits financially. There's plenty of scope for win-win there.
The issue on this occasion appears to be that Duncan's agent doesn't want his client to go through any of that process and instead wants him to be sold at age 18 to a foreign club.. because he's way more likely to get first team minutes there? Without knowing enough about just how good Duncan is (from what I've seen in pre-season friendlies, he's more than good enough to have a professional career somewhere, but far from a guarantee to be a top tier footballer, let alone at an elite club), it seems like this is a lose-lose situation. The club gets none of the opportunity to actually invest in the player's career path, and the player goes overseas where he has far fewer friends and none of the language to guide and advise him. Unless of course his agent knows something we don't, and Fiorentina is a better developer of young talent than Liverpool.
It's really a lose-lose-lose, because even the agent ultimately gets a cut of a tiny transfer fee, whereas if he had allowed Duncan to follow the path of his colleagues, it's pretty clear that there's a much bigger payday down the track.