When Harry leaves the Burrow to go to Diagon Alley by Floo Powder in CoS, he ends up in Knockturn Alley. He sort-of pronounces it wrong:
‘D-Dia-gon Alley,’ he coughed.
How does that equate to "Knockturn Alley"?
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After being overloaded with advice from all the Weasleys, he stutters while trying to say "Diagon Alley" through a mouthful of ash and ends up slightly off-target, landing in Knockturn Alley instead. The reason he ends up in Knockturn Alley (which admittedly doesn't sound much like "D-Dia-gon Alley", nor the "diagonally" of the film) is that he almost made it to Diagon Alley, but his pronunciation sent him slightly off-target to the next street.
This is covered in the book itself:
‘Well ... all right ... you go after Arthur,’ said Mrs Weasley. ‘Now, when you get into the fire, say where you’re going –’
‘And keep your elbows tucked in,’ Ron advised.
‘And your eyes shut,’ said Mrs Weasley. ‘The soot –’
‘Don’t fidget,’ said Ron. ‘Or you might well fall out of the wrong fireplace –’
‘But don’t panic and get out too early, wait until you see Fred and George.’
Trying hard to bear all this in mind, Harry took a pinch of Floo powder and walked to the edge of the fire. He took a deep breath, scattered the powder into the flames and stepped forward; the fire felt like a warm breeze; he opened his mouth and immediately swallowed a lot of hot ash.
‘D-Dia-gon Alley,’ he coughed.
An old wooden street sign hanging over a shop selling poisonous candles told him he was in Knockturn Alley. This didn’t help, as Harry had never heard of such a place. He supposed he hadn’t spoken clearly enough through his mouthful of ashes back in the Weasleys’ fire. Trying to stay calm, he wondered what to do.
Harry and Hermione looked around; sprinting up the crowded street were Ron, Fred, George, Percy, and Mr. Weasley.
"Harry," Mr. Weasley panted. "We hoped you'd only gone one grate too far ..." He mopped his glistening bald patch. "Molly's frantic - she's coming now -"
-- HP and the Chamber of Secrets, Chapter 4: Knockturn Alley (emphasis mine)
If you pronounce anything wrong when using floo powder, and are not used to it, you could end up literally anywhere.
It was Harry's first time using floo powder, he stuttered when saying the destination. When using floo powder you are always supposed to speak clearly so that you don't end up in a random place. Anyways, Harry stuttered while saying the destination. ‘D-Dia-gon Alley,’ he coughed. Then, because he stuttered he ended but really close to his destination, the alley right next to Diagon Alley. A quote from the book
'He supposed he hadn’t spoken clearly enough through his mouthful of ashes back in the Weasleys’ fire'.
Because when using Floo Powder you need to say where you are going very clearly. Harry tried speaking the words "Diagon Alley" with a mouth full of ashes. Instead he said “diagonally”. I'm guessing he went "diagonally" instead of going "straight" to where he wanted; which lead him to a place where no one wants to go.
He says it good enough, but if you read what Ron and his brothers had told him, Ron said, "don't fidget". While, George and Fred told him not to panic, which he had done both. So he fell out too early, which was obviously the wrong fireplace, which was both of the consequences of his actions. I'm also thinking the reason he panicked was because he had choked and knew he mispronounced Diagon Alley.