When you have your own private name servers it looks like you are running the hosting company or have your own dedicated hosting. Instead of people seeing your web hosting companies name servers they see your private name servers. I also like this if you have multiple sites in the same niche and are heading off in a black hat route, you don’t want to competitors to see that all the sites are probably belonging to one person.
Also If you sell hosting and you do not want your customers to know who your web host is you would want your own private name servers.
This isn’t particularly relevant in my case, but another reason for having private name servers is that if you host multiple domain names then you can update the I.P. address for the private name servers once instead of having to update the name servers for multiple web sites.