This takes place near the beginning of Harry's first year, sometime before Halloween. It fits in at a lot of different spots. This, to me, is a logical excuse why Harry doesn't try at potions.
Harry stared at his book, unable to find the seventh purpose of the ingredient. He thought of everything he could; he even checked out a book from the library hoping to find the answer, but it was no use.
Harry Potter knew what he should do: go talk to the professor so he could be pointed in the right direction, but the problem there was, Professor Snape hated him. The few times he had class with the Potions Master not only proved it, but also let him know that it wasn't going to change.
Sighing, Harry stood up, grabbed his paper and potions book and headed out of the common room to find the dungeons, a sick feeling in his stomach. He knew this was not going to go well, but he didn't have much choice in the matter. Ron had refused to do the assignment until later, so he wouldn't be able to help at all.
Down in the dungeon, Harry stopped ten feet away from the professor's office as the man exited. Snape spotted Harry immediately.
"Look what he have here: a trouble maker," Snape sneered dangerously. "What are you doing down here, Potter?"
"I was wondering . . ." Harry trailed off for a bit.
"Well? I don't have all day, so make it quick or go back to your tower."
"Er . . . I couldn't find the seventh purpose, I was wondering . . ."
"Of course, I should have known. The Famous Harry Potter wants someone else to do his homework."
"No, of–."
"The homework is to be done on your own. Two points from Gryffindor for trying to cheat. Now, leave," Snape snapped, and Harry glared at him before turning away. He walked quickly, but not so quick that Snape could take points off for running. The dark haired man seemed worse than Uncle Vernon, and from Harry's point of view, that was saying something.
Fine, thought Harry. If he doesn't want to help, then I don't care. I'll see if that Hermione girl will help. If not, I'm leaving it as it is. That decided, Harry slowly made his way back to Gryffindor tower to tell his fellow house mates to never ask Snape for homework help. The point deduction and the ridicule wasn't worth it.