|This ought to keep them out of trouble!|
My theories will be supported by the fact that in the manga, regular Titans when they eat a Titan shifter gain the Titan’s shifter’s powers. They gain the ability to shift from Titan to their original human forms, and possibly the other powers as well. Also that all Titans were humans turned into Titans by some hidden science.
So why do Titan eat humans?
I think they eat humans due to an instinctual drive to be able to become human again, the only way for them to be human again is to gain the power of a Titan shifter to transform from Titan to human and back again. They eat every human they find in “hope” that one of them is a shifter, and they can end the hell of being a regular non changing Titan. It’s not an intelligent desire though, just a basic animalistic desire. As a Titan they have no morality and barely any intelligence, so they eat as many people as they come across and when they run out of room in their stomachs they throw up the remains of the people they ate in order to keep trying to find one that may be a shifter. But when they come across a shifter in Titan form they drop everything and rush right to it, ignoring the humans in order to devour it.
The Armored and Colossal Titan are not allied with the normal Titans, in Titan form they are in much greater danger of being targeted, because regular Titans are able to tell them, and their screams apart.
Also i don’t think Titan shifters can eat other Titan shifters and gain their ability. They’re limited to just one extra power each.
What did Eren’s father do to Eren?
I think the ability to change people into regular Titans is still known to select scientists, including Doctor Yeager. But the ability to create Titan shifters is lost. I think it’s possible that Doctor Yeager was a Titan shifter himself. He turned his son into a regular Titan and let his son eat him, giving his son the Titan shifting ability. Along with the special power he carried, the Coordination power.
How do the Titan shifters extra powers work?
I think the extra powers that shifters possess in Titan form get stronger with each generation. Meaning every time a shifter gets eaten by a Titan, the power gets stronger with it’s new owner. For example I believe a regular Titan version of Reiner Braun ate the previous armored Titan, and in the process gained the shifting ability and also gaining stronger armor then the previous Armored Titan. The same is true of the other shifters, the Colossal Titan gets bigger with each generation, the Female Titan gets harder crystal skin generation, The Dancing Titan gets increased agility. The power of Eren’s Titan form, coordination, gets more powerful with every generation.
Eren’s Titan form has the power to control other Titan’s minds, and perhaps people’s minds as well. Eren is shown having dreams about memories of a woman he never met before, but the dreams or from the woman’s perspective. I think that woman is a previous Coordinate Titan shifter, possibly the one Eren’s father had to eat. This same woman was a friend to Historia but had the ability to alter Historia’s memory.
I think the reason that this woman nor Doctor Yeager was able to end the Titan attacks was because their ability to control Titans wasn’t strong enough. Maybe they could only control one or two at a time or none at all. But now with Eren the ability is strong enough to control groups of Titans. I think the woman and Doctor Yeager gave their lives knowing they’d have to for the future of humanity.
I also think the previous Female, Colossal, and Armored Titans allowed themselves to be eaten to order to ensure that the abilities would be stronger, so the new generation can have the power to find the coordinator Titan.
Why did the Colossal and Armored Titan’s attack the wall?
They did it to draw out the Coordinator Titan, at the time of the first attack was Doctor Yeager. I’m not sure if they knew who the Coordinator Titan was, or is the attack on Shinganshina was just a random attack. I think it’s possible that they suspected Doctor Yeager and targeted his home city for that reason. Though because he was out of the city, the knocked a hole in the inner gate so they can force him to act at a later time. Before the attack on Trost they suspected that he might have passed his power to his son. So they attacked where Eren was located, and when he did transform no further attack was necessary, and they focused efforts on capturing him.
They wanted to try and convince Eren to join them to control the Titans, not trusting the the corrupt government in the walls would use Eren for the greater good. If Eren refused they could feed him to a normal titan and hope the new shifter would be more cooperative. I think Reiner, Bertolt, and Annie are trying to act for the heater good in ending the Titan menace, even though it does cost many lives.
edit 10/11/2014: Newest chapter confirms that Titan Eren did eat his father. And one of the flashbacks to seem to be of Eren's father in Titan form eating the mysterious woman in Titan form.
Here's what I think is happening in the flash back, everything is a sequence of events as seen by Eren's father, until he's eaten by Titan Eren. It occurs when Eren's father was away during the fall of wall Maria. Eren's father has the knowledge to create the drug that turns people into regular Titans and he's called by the Reiss (the real royal family) to the cave under the chapel to turn a member of the family into a Titan so that person could eat the the mysterious woman Titan shifter who has the Coordinator power. It's done in order to keep the memory altering power and possible Titan controlling power in that family. Eren's father is tired of maintaining the status quo and starts his plan to enable his son to finally lead humanity outside the walls. Eren's father injects himself with the drug turning into a normal Titan. The mysterious woman (The dark haired one) turns into Titan form to fight Eren's father but she's defeated and eaten by Eren's father's Titan form, gaining her abilities. Eren's father isn't finished yet, he kills everyone else there and destroys the chapel. He heads back home, finding out about the attack on the wall by the Colossal and Armored Titans. Later he gives his son the key and turns his son into a regular Titan. Eren eats his father and gains his powers. Eren probably erases his own memory of the event.
This was Eren's father's sin, stealing the Coordinator power from the Reiss family. They intend to get it back probably, by turning Historia into a Titan. I don't think Historia was aware of this, she looked rather shocked, after seeing the memories in Eren.
Also it might provide extra explanation of the attack on wall Maria, the Colossal and Armored Titan attacked Eren's father's home town in retaliation for him taking that power. Or they're opposed to the Reiss family and attacked when Eren's father took out the family, finding it the perfect time to start their plans.