The author is being cute.
He is listing reasons that many people offer for not starting a business.
So the reasons are reasons not to start a business. If his goal was to stop you, he could just list those reasons.
But he takes each reason and considers it and tells you that it should not stop you. Or he gives ways to work around the reason. Or he gives analysis of why the reason does not apply to you. He is showing that these reasons do not have to stop you, and in some cases should not stop you.
So the list of reasons would be "Why to not start a startup." Notice only one "not." All these horrible things could happen. And if you accept that list of bad things then you should not start a startup.
And then he puts his analysis on it. And he shows each reason is, for some reason or in some way, not a good reason to be stopped. So the essay becomes "Why to NOT not start a startup." That is, he is saying that starting a business should not be stopped by the list of reasons he has analyzed.
Notice he is NOT saying there are no other reasons. He is saying the reasons he lists should not stop you.