Attack on Titan features several Titans that are deemed "Abnormal," but why only some of them become that way is an interesting question. The first Abnormal Titan appears after Bertolt Hoover, in his Colossal Titan form, breaches Wall Rose in a second attempt to devour all of the humans inside. When headquarters becomes completely overrun with Titans, cadets are unable to resupply and all seems lost. Suddenly out of nowhere, the Abnormal Titan appears and begins to fight off the hordes of other Titans, allowing Jean and the other cadets to enter Trost headquarters to resupply. At this point in the series, this mysterious Titan's behavior is strange, to say the least.
Attack on Titan season 3 reveals the Titan's origins, and it's shown throughout the anime that there are different types of Titans wreaking havoc on Trost and the rest of the Attack on Titan universe. Abnormal Titans are a type of Pure Titan, or Muku no Kyojin, originally formed from people known as the "Subjects of Ymir." Pure Titans are normally incapable of emotion, human thought, or comprehension, leading them to attack and devour the closest thing in sight. Abnormal Titans, on the other hand, have shown that they are capable of speech, emotion, and strategic attacks.
Abnormal Titans are able to exhibit these strange behaviors because they are being controlled by Titans who have the ability to do so (such as the Founding Titan), or they have held on strongly to specific attributes that reflect their previous life and the things they might have cared about. This may explain why some Abnormal Titans don't eat humans. Take, for example, Connie Springer and his mother. After Connie returns home to Ragako, following the wake of the Titan's decimation to the village, he comes upon his mother laying on top of the rubble of their home. Even though she is now a Titan, Connie's mother finds the strength to mutter to Connie "welcome home." This interaction has great implications for the relationship between the Titan form and the human host. It means that Abnormal Titans that can't attribute their actions to outside control must have some former memories or cerebral attachments to the humans they once were, which causes them to think, feel, speak, and even see people as more than just prey.
There are other interactions that highlight an Abnormal Titan's intelligence and allude to the Titan's connection to its former human attributes. In Ilse Langnar's Notebook, a small storyline featured in the 5th volume of Hajime Isayama's Attack on Titan manga, Ilse's scout team is attacked and she runs into a forest. Ilse is cornered by an Abnormal Titan. The Titan verbally greets Ilse and even bows in respect. Unfortunately, after an emotional conversation with the Titan, it turns on Ilse and kills her. However, it is worth noting that the Abnormal Titan displays great emotional turmoil in its choice to decapitate Ilse and cries after killing her. It even stashes Ilse's corpse away rather than eating it.
The final Abnormal Titan in Attack on Titan is most likely Rod Reiss, though this is obviously yet to be seen. Attack on Titan season 4 has plenty of questions that need answering and part 1 left off with Eren in his Attack Titan form, waiting for Reiner's retaliation. With the interesting part that Abnormals have played in the Attack on Titan series, one can only hope that the Abnormal Titan's behaviors and origins can be further explored. Connie's interaction with his mother especially, as well as Ilse's experience, shows why some Titans deviate from the rest in interesting ways.