Because the number you're reasoning about is the number of spears he wished for, not half the number he wished for, so mathematically, the logic holds for 3 different possible wished for integer values.

To arrive at precisely 12002 you need to make a further assumption which nobody has explained so far.

Also, a minor point, but that he wished for an integer number of spears is another assumption. Albeit a very reasonable seeming one, it's an assumption none the less. He could have wished for 12 thousand and π spears, for example. And no, I have no idea what you'd do with that ~14% of a spear.

If this were an SAT question, and upvotes correlated to what people were answering, well, the majority got this question wrong.