The story is simply not believable, and if she's lying, why? The logical, reasonable answer is: to cover up a murder.
Which is nothing like
evidence that she committed a murder.
Why have various members of her family changed their stories, been uncooperative, and possibly lied at various times during the investigation?
The logical, reasonable answer is: to hide something. To cover up facts about the death. Or to protect Casey. Or to protect the father. Or something else.
"Casey is a liar" would be more persuasive if she were the only whackadoodle in the family, telling lies when everyone else in the family and the investigation are paragons of good citizenship. Sadly, this is not the case. Something aint' right with them folks.
Also sadly, what the prosecution also doesn't have is the air-tight forensic case that they gave the impression of going into the trial. Their forensic expert has been contradicted by other credible experts; the circumstances of the discovery of the body - in any area that had been repeatedly searched near the parents house - have been called into question, etc. This is, of course, what trials are for.
And then there's her mother testifying that she was the one who searched for "chloroform" on the Internet rather than Casey...well, she's probably lying, but she's not being charged with murdering anyone. Casey's boyfriends may be lying about allegations of sexual abuse by Casey's father...but they're not being charged with murder. Either Casey's father or the woman he visited and texted with during the search are lying about having/not having an affair and whether or not he told her that Caylee's death was accidental...but the logical conclusion, in either case, does not seem to be that they were involved in the child's death. The guy who discovered the body either lied when he said that he didn't move the child's skull or lied later when he contradicted that on the witness stand, but...well, you know...
"The accused acts guilty" is a pretty sad standard to have to fall back on to justify convicting someone of a capital crime. But of course, juries do and always have, as we've been discovering with dismaying frequency since the advent of DNA evidence. There's no DNA evidence in this case, of course...there's not even sufficient evidence to determine a cause of death.