The decision to not raise angel investment is ultimately a personal one based on the financial needs of your business, your end goals, your style of management, the sector or industry your business is in and whether or not you want to answer to investors.
The countless posts on the web that frame angel investment (or even venture capital) as a binary decision-making process in which businesses should or should not take angel investment ultimately are a disservice to you. Your business and you are unique in your needs so the decision to seek angel investment is one you need to make that is best for you.
Moreover, many posts speak of entrepreneurs choosing between angels or venture capitalists and fielding innumerable funding choices or entities. The reality for most entrepreneurs is that battling term sheets are not the norm and so an angel (or a VC) may at times represent your shot at giving your idea a fighting chance or packing it in.
With those disclaimers in place, here are some reasons cited not to raise angel investment. Again, these are given so you can go in with your eyes open and are not meant to dissuade you from seeking angel investment.