For many smaller websites shared hosting is perfectly capable of providing an acceptable experience to its users, but what happens when your site begins to grow? Most companies have shared hosting. Do you have any idea which websites are identified with you? The content of any number of the sites could lead to the whole IP address being blacklisted by search engines. The way any of the sites are coded could put a significant drain on the already spread-thin resources the server has leading to unexpected downtime.
That is a reassuring thought for you, our dedicated server protects your interests!