Most frequent realms for post-human rebirth I read the following extract from the book "The Workings 
of Kamma", produced by the Theravada monastery "Pa-Auk Tawya Sayadaw"


  Rebirth in the human world is always because of wholesome kamma. None-
  theless, among the great majority, the uneducated ordinary people, conscious-
  ness is rooted predominantly in greed, hatred, and delusion. Only occasionally do 
  wholesome consciousnesses arise. And among the uneducated ordinary people, 
  delusion is very deep. That is why, when human beings pass away, they are al-
  most always reborn either in hell, the ghost world, or the animal world.


I have several problem accepting these views. Of course, what i am about to say is very subjective and i certainly do not claim to be an enlightened being and know everything.

The first is that i believe that there is a powerful continuity between rebirths. So my personnal and subjective understanding is that when we look at a person, we can easily guess what type of person he was in a previous birth. Most importantly, the level of virtue, intelligence, strong tendencies, evolve very little from life to life for most people as they don't engage in serious self-study or self -improvement and indulge in their pre-existing tendencies. So the current level of consciousness exhibited by ordinary people should reflect their previous level of consciousness in their previous existences. Which means that human birth doesn't require more positive kamma than what most people exhibit. Some of them might have produced better karmas in the past. Some of them might have produced worst karma in the past. But overall, we should grossly be able to determine the level of virtue necessary for human rebirth by observing humans.
Otherwise, this makes no sense, at least to me.

Also, animals are described as experiencing mostly greed, hatred, delusion. I think this is seriously off.
Animals are instinct driven and regularly obey their instincts, but many of them are often peaceful and detached. Would you say a wild horse experiment greed, hatred, fear on a constant basis? Yes they sometimes do and act like animals are supposed to. But this is a minor part of their lives. Many animals are peaceful and worry-free, even though their lives are harsh and short. Turtles are another exemple of a peaceful animal which can live longer than humans.

Would experienced buddhists agree with the passage quoted, and if yes, what arguments would they provide to change my analysis?
Then the Exalted One,
taking up a little dust
on the tip of his finger-nail,
said to the monks:

"Now what think ye, monks?

Which is the greater,
this little dust I have taken up
on the tip of my finger-nail,
or this mighty earth?"

"Greater, lord, is this mighty earth.

Exceeding small
is this little dust taken up
on the tip of the Exalted One's fingernail:
it cannot be reckoned,
it cannot be compared therewith.

It does not come to the merest fraction
of a part of it
when set beside the mighty earth, -
this little dust taken up
on the tip of the Exalted One's finger-nail."

"Just so, monks,
few are those beings that are reborn among men:
more numerous are these beings
that are reborn other than men.

What is the cause of that?

It is through not seeing four Ariyan truths.

What four?

The Ariyan truth of Ill,
the Ariyan truth of the arising of Ill,
the Ariyan truth of the ceasing of Ill,
the Ariyan truth of the practice that leads to the ceasing of Ill.

Wherefore, monks, an effort must be made to realize:

'This is Ill'.

'This is the arising of Ill.'

'This is the ceasing of Ill.'

This is the practice that leads to the ceasing of Ill.'"

—http://buddhadust.net/dhamma-vinaya/pts/sn/05_mv/sn05.56.061-070.wood.pts.htm

and the suttas that follow.