Professor Slughorn did not teach Sirius Black because Sirius was a student at Hogwarts during the time when Slughorn was not a teacher at the school. Slughorn was not part of the Hogwarts staff during Sirius's time as a student, so he did not have the opportunity to teach him. Sirius attended Hogwarts during the time when Professor Slughorn was not teaching Potions, which was the subject he was known for. **

Horace Slughorn is a complex character in the Harry Potter series. He is portrayed as a skilled and knowledgeable wizard who values connections and networking. However, his tendency to favor students who are well-connected or have prestigious backgrounds can be seen as a flaw in his character. Overall, Slughorn adds depth to the story by showcasing the importance of relationships and influence in the wizarding world. **

Tom Riddle and Slughorn had a complex relationship. Slughorn was initially drawn to Tom Riddle's exceptional magical abilities and potential for greatness, and he took a special interest in him, even going as far as to invite him to join the Slug Club. However, as Riddle delved deeper into the dark arts and began to show signs of his true nature, Slughorn became increasingly wary of him. Despite this, Riddle was able to manipulate Slughorn into sharing important information with him, ultimately using it to further his own dark ambitions. **

Dumbledore brings Slughorn back to the school because he wants to obtain a memory from him that is crucial to understanding Voldemort's past and his Horcruxes. Slughorn possesses a memory of a conversation he had with Tom Riddle, in which Riddle asked about Horcruxes. Dumbledore believes that this memory is key to understanding Voldemort's immortality and defeating him, so he persuades Slughorn to return to Hogwarts in order to retrieve it. **

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It is possible that some of Tom Riddle's former teachers may regret their past behavior towards him, as they may have missed signs of his dark nature and potential for evil. However, it is also likely that some teachers may not feel remorseful, as they may have been unaware of the extent of Riddle's dark intentions or may have believed they were doing their best to guide and educate him. Overall, it would depend on the individual teacher and their perspective on their interactions with Tom Riddle. **

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It is possible that some of Tom Riddle's former teachers may regret their past behavior towards him, especially if they realize the extent of his dark and manipulative nature. However, others may not feel remorse, as they may have been unaware of the true extent of his actions and intentions. Ultimately, it would depend on the individual teacher and their level of insight into Tom Riddle's character. **