You are on facebook and linkedin and so are millions of other people. All facebook and linkedin profiles look alike after a while and it doesn’t set you apart from the crowd.
Blogging shows off your command of the English language and your ability to organize your thoughts and pen them. If you’re a business person, having your own blog shows your customers and associates that you’re capable of stringing words together in a coherent fashion.
Even better, a blog shows you have established, and continue to nurture, your own unique voice. What that voice speaks to is up to you: Your chosen profession, a hobby you’re passionate about, or just your life in general.
It’s your contribution to the social space. Yes, social media has a lot to do with sharing the work of others (particularly on Twitter). But, people will want to get to know you too, especially if they like what you curate for them or come to look forward to your comments on their own work. A blog is a home-base for all things YOU. They can focus on one particular aspect of your personality or profession (which is why you often find people with multiple blogs). Having your own blog shows you can dish it out AND take it.
You’re controlling your own online reputation. If you’re not blogging, or using other social tools, then you can’t pro-actively manage your digital reputation in any way. Offering an authentic, official perspective of who you are as a person ensures that people have something else to look at in the event a person with a vendetta tries to digitally ruin you.