You shouldn't. Knowing will not change the situation (though it may satisfy your curiosity), while telling you could be problematic for many reasons. Asking for justification made above your pay grade will also likely paint you in a bad light.
Effect Positive Change
If you liked the previous boss, but have issues with the current one, put your effort in to improving that relationship. No amount of nostalgia over your previous boss will bring him back, and letting your boss and the CEO know that you preferred the older boss is not going to make that working relationship any easier.
If there are specific things about the way the previous leader worked that were beneficial to the team, work to re-implement those with the new boss by explaining what worked, why, and what the benefits were to the team. Don't put it in context of the old boss, put it in context of creating a more productive team moving forward.
Do Not Dwell on the Past
There are a trillion reasons your old boss could have been fired, and knowing them will not improve your work experience or give you closure. What if he was fired because:
- He was embezzling company funds
- He was sexually harassing the secretary
- He lied about his credentials/education/work history
- He put a man in the hospital after a bar fight, etc.
Would knowing any of these things be beneficial to you? Would it be beneficial for the company to tell you? Would learning about an indiscretion satisfy you and help you focus on your work, or just make you more curious about the details?
What happened happened, sometimes things are better left unsaid.
Know Your Place
Whatever reason he was fired for, it was decided by people in charge of managing your managers. This is well above your pay grade.
The decision was likely made behind closed doors, with far more information than you have, and was probably not made lightly. What will reopening that wound with incomplete information accomplish?
If you go up to the CEO and say, "We really liked our old boss, and want to know why he was fired" what you are essentially saying is, "Despite not having complete information, we think that you made the wrong decision, and expect you to justify your choice to us."
Chances are you wouldn't make that demand if your boss had switched careers without telling you where he was leaving or why, so what makes you think that in the more sensitive context of someone being fired this will be a good idea?