When I fire someone, or lay someone off, I make a decision about what to tell the rest of the staff. With a firing, sometimes I am very open about the performance problems the person had and the steps I took to work on them with the employee - especially where others were aware the employee was struggling; other times I say less on the matter. With a layoff I am always clear on where the company stands but I may not go into details about who was chosen beyond "it was based on the skills mix the company needs going forward." I have enough experience to know that coworkers are going to be curious, and a little worried for themselves, so we would often have a short meeting that was focused on that aspect of this - how does this affect the remaining workers?

I can tell you this - if I've decided not to discuss why I fired someone, being asked why I fired someone would change nothing. Asking almost implies that I hadn't considered the possibility others are curious or worried, and of course I have considered it. As a result I would be a little offended. If you're young as well as a new hire, I would chalk it up to inexperience. If you're experienced enough to know better, it would lower my opinion of you that you're pressing for details on a decision of mine either out of personal curiosity or perhaps because you think I made a bad decision.

I recommend you ask questions about yourself not about the people who have left. Are there layoffs underway and are you at risk? Will you be picking up new duties to cover some of what the terminated people used to do? Is the focus of the company or department or team changing? Are the standards of good performance changing (perhaps because of a new manager) meaning you should adjust your behaviour? (Typically that gets announced, but you can ask if you like.) Questions about yourself are not as invasive or curiosity-based as questions about another person.