The criteria for speedy deletion are exclusive. That means, if the reason you wanted the article deleted isn't on the list, I can't delete it. Usually, I'll mark the article for PROD, take it to AfD or tag it for clean-up. And I'll give a reason in my edit summary for why I'm doing it. Please remember that other admins will often just de-tag and do nothing else, so you've got two for the price of one here.
If you gave no reason for deletion, or lied in your reason, then you can nominate again with a reason (or a correct reason).
If you gave a reason and I didn't agree, well, that's how things are. Some things that are an "obvious" delete are not included in the criteria for speedy deletion and must take a slower path. Things like notability are not so subjective - if credible notability was asserted in the article, then it isn't a speedy delete - you may hate Harry Potter, but the person translating the books into Basque has a degree of notability, especially if they've also done something else as well.