Harry has his first dream about Voldemort. (crucial to what happens in Order of the Phoenix).

You can see how Voldemort tries many ways to persuade Harry to be around Slytherin-y people.... firstly by asking, then by trying to force him, then by showing the consequences of not choosing the answer that Voldemort wants you to have.

Maybe Snape was so difficult to Harry throughout his entire schooling - to ensure that Harry would NEVER want to be in slytherin... where there would have been a much more lenient approach or concern about Death Eaters and Voldemort...