After a while, there was a serious argument on the subject between Slytherin and Gryffindor, and Slytherin left the school." - That tells me Tom Riddle being a half-blood would not have been expected by Slytherin to attend Hogwarts in the first place - let alone be his heir.
Maybe I'm just hearing the wrong comments, but it seems that Slytherin is considered a dark house by almost everyone. I know when both reading the books and watching the movies, I always had a fee...
Harry's first year: Slytherin v Gryffindor (Harry's first match) - Gryffindor wins Slytherin was ahead 40 - 20 before Harry caught the Snitch. Gryffindor v Hufflepuff - Gryffindor wins How much either team managed to score was unclear, but the game lasted less than five minutes as Harry caught the Snitch in record time and won the game.
harry potter - Why did the Slytherin team opt for size over skill ...
Was Salazar Slytherin a Dark Wizard? E.g. we know he refused to teach Muggle-born magic. But was that because "it's a bad idea"; or for "Muggles are subhuman and need to serve the wizards" reason...
harry potter - Was Salazar Slytherin a Dark Wizard? - Science Fiction ...
If every former Hogwarts student who goes bad was in Slytherin, why has Hogwarts kept the house over the years? Why not disband it?
harry potter - Why did Slytherin House not get disbanded? - Science ...
harry potter - How can Ron know that Voldemort was in Slytherin if ...