The charge of murder requires three elements to be proven:
1) Cause the death of another: You have to specifically show beyond a reasonable doubt that the accused did indeed caused the death of the victim in question. The prosecution had no evidence that conclusively proved that Casey Anthony killed her daughter. There are too many questions that remain unanswered. Keep in mind that the specific cause of death is not required. We don't have to know how someone died to know that someone else caused their death, although it does make it easier to prove.
2) With prior planning (premeditation): You have to show that the accused specifically planned the death of the victim. The prosecution could not show this either.
3) Mens Rea/With intent (malice): You have to show that the accused intended to cause sufficient injury to result in the death of the victim in question.
Note that the actual cause of death is not required. Nor is motive required. The two can make proving the above three a helluva lot easier, but they are not necessary to prove the above three.
For both 2 and 3, 1 has to be shown first or there's no case. If you can't show 2 nd 3, but you can show 1, then you can maintain that it was manslaughter (which she was also charged with), but because they could not show 1 beyond a reasonable doubt, there was no way that manslaughter was going to stick. Because neither of them were going to stick, the child abuse wasn't going to stick either. I'm thinking the manslaughter was a backup plan in light of the thin evidence of murder, and the child abuse charge was going to be icing on the cake in the event that one of the other two stuck. It didn't work out for them.
The fact that she didn't report the child missing is not sufficient evidence to prove murder. You have to prove Actus Reus, the guilty act, the actual murder. Not mitigating circumstances that leads you to suspect someone of murder, you have to prove the actual murder, the actual act of the accused taking someone else's life with intent and prior planning. Prosecution could not do that, and that's why she was acquitted.
Do I believe she killed that child? Yes, I do. Does it matter what I think? No, it doesn't. It doesn't matter what anyone thinks, it doesn't matter what any analyst thinks, it doesn't matter what any news anchor thinks. A jury of her peers has spoken and acquitted her on the three charges.
If the prosecution had better evidence, a better all around case, then Casey Anthony would be facing the possibility of death row.
It sucks, but that's the way it goes. Maybe someday they'll figure out what really happened to that poor child. Unfortunately, if she did kill her own child and they learn precisely how to prove it beyond the shadow of a reasonable doubt, tehy won't be able to try her again.