At the end of the day, walking away is the player's decision. And, since they are the one putting in the time, making the effort, enduring the sacrifices, jumping the hurdles, it is, and should, be their call. It's their baseball career, not ours.
I think the challenge as a parent is that we have been so involved as the ride was happening, and usually have a love of the game, that it's hard for us to see it end, especially if they are walking away and we feel like there's more gas in the tank and still future chapters for the story. And, I'm sure (whether they want to admit it or not) that some parents feel like their son playing baseball is a reflection on them and giving them (the parent) skin in the game - and, losing that is a blow to their self-esteem.
But, what if the relationship wasn't baseball? What if it was something else.
What if your son wasn't ending his baseball playing relationship after 16 years? What if he was ending a 16 year relationship with his girlfriend because he felt like it had stalled, they had changed or it had just run its course? What would your reaction be as a parent?
You would still be sad for your son. Nobody likes to see their kid go through difficult times. And, if he was with someone for 16 years, you would also feel the void because she had become like a member of the family.
But, would you lament the ending like some take ending baseball so badly? Probably not. And, you would support your son and easily understand that it was his relationship and only he would know if it was still worth maintaining or ending. You would be there for him, respect the decision and probably be a little grateful that he didn't keep doing something just because he was doing it forever. And, you probably would be proud of him for putting himself on a new path that would be the best for him, personally.
That said, if your son has made the decision to walk away from playing the game, it's his right to make that call and you should respect it and support it. And, it's OK to be a little sad. But, you should also be grateful that your son is doing something that he feels will put himself on a better path for his future.