First we have Aragog an acromatula, which is a large spider with eight eyes, talking abilities, pincers, and is carnivorous. Hagrid acquired an acromantula egg after his father died while he was in school. He hid the acromantula that he named Aragog in Hogwarts. Hagrid's lack was filled by this relationship. During this time there was a monster in Hogwarts and Aragog asked to flee, yet Hagrid wouldn't let him. Hagrid was very dependent on Aragog and we see this when Aragog is accused of killing students. Hagrid defends him and is expelled from school and has his wand snapped. Hagrid is still able to work at Hogwarts and continues to as we see in the Harry Potter series. Even after all of that he still visits Aragog and takes care of him in the forbidden forest.
Below is a scene about Hagrid being turned in for owning Aragog.
Below is a scene about Hagrid being turned in for owning Aragog.
Then in The Sorcerer's Stone Hagrid takes in a Norwegian Ridgeback dragon. This species of dragon is aggressive to his own kind and attacks large land mammals, and gain the ability of fire-breathing faster than any other dragon. Hagrid decides to take the dragon egg and raise him in his hut. This doesn't make sense at all considering he won't be able to take care of him forever and it is illegal for him to own this dragon. Hagrid isn't thinking clearly his desire is causing him too repeat his past. This is the same thing that happened with Aragog.
Below is the scene where Norbert hatches.
Below is the scene where Norbert hatches.
Grawp is Hagrid's step brother who he took home with him because he was being bullied by all of the other giants for being too small. We meet Grawp when Hagrid is asking Harry and Hermione to watch over him, because Hagrid is sure he will be getting fired. Hagrid is also being abused by Grawp, but brushes it off knowing he doesn't mean it. Hermione is the one to point out that "He's been hurting you all this time, hasn't he? That's why you've had all these injuries!" Rowling describes Hagrid as bruised and blood dripping from his nose. Hagrid's desire is overcoming his judgement again. He doesn't see how unhealthy this relationship is. I think Hagrid could have gone about this in a safer way.
Below is the scene where Hagrid introduces Grawp.
Below is the scene where Hagrid introduces Grawp.