No is a valid answer, but rarely a useful one
No is most certainly an answer. However, simply posting the word "No", or "No, you can't do that." doesn't add any value, and you should probably expect to have your answer downvoted. You haven't added anything to the question that the simple lack of a "yes" answer already shows. However, if you provide some justification for how you arrived at your "no" answer, you might even end up with a good answer. This will be rare, though, as proving a negative is a pretty tricky business.
So, short version, a "no" answer is valid and shouldn't be deleted any more than an incorrect "yes" answer should be deleted, but someone who posts one without backing it up can probably expect some serious downvotes to occur.
Closing a question because you think it has no answer turns close votes into "No" answers that can't be argued with.
The separate idea that a question should be answerable to remain open is a very problematic one. It implies that you are certain the answer is no, and rather than provide that "No" as an answer with some justification, you're just going to skip all the work of convincing anyone and simply hit the close button. It effectively turns your close vote into a "no" answer that other users (without enough rep to vote to reopen) are not allowed to argue with. This makes your close vote amount to a really hefty version of the crappy, non-justified "no" answer that I just described as low quality above. This is worse, even, because if 4 people agree with you, no one can even post a "yes" answer until they gather up enough reopen votes.
In the hypothetical scenario that a question is closed as unanswerable and then someone comes here and has an answer, we now just placed the burden upon them of finding 4-5 other people that they have to convince to reopen it before they can post their answer. Where's the value in that? And how are they going to convince those people... their main weapon would be to actually post the answer and let it speak for itself. But they can't. So what... they have to start a meta explaining that they have an answer and that it should be reopened? A lot of people at that point, particularly newer users with low rep, will just shrug their shoulders and walk away. Who are we serving by doing this? What was the harm in simply leaving the unanswered question open? We're turning this into a lot of extra work and creating a huge potential for comment wars and drama for no reason.
Are you sure your problem with the question is really that it doesn't have an answer?
A lot of times, I think the problem is that the question is ambiguous or a pointless thought exercise, and the reaction of "There's no answer to that!" seems like a quick and dirty way to get it closed. But answerability is a terrible metric for topicality, and we should instead look closer at what types of questions we're really trying to avoid here.