On the soft skills side a DBA is a bridge between so many layers of business, a dba can touch on development, operations, and the individual business units and internal customers. It requires being able to speak all the different languages and so being able to work well with everyone is a requirement. (I.E. Communicate)
On the technical side a DBA is sometimes called to fix or solve problems so far outside of just the database that a DBA needs to understand the fundamentals of all aspects of the IT world. Development, QA, Servers, Disks, Networks, and End-User products. (I.E. Technical Jack of All Trades)
On the personality side a DBA needs to be proactive and aggressive at getting the job done when required. If a bunch of customers are threatening to leave because production is slow, a DBA needs to be leading the charge at solving those problems, especially when the application is heavily database backed.
So in my mind, a highly technical social person are the best DBAs. The type of person who starts out IT but goes into IT Management and being a DBA is a stepping stone of transition. The last stop to verify they have a full technical understanding, but the soft skills for management, and being able to quickly get data from a database is a good skill into the analytical work a Manager sometimes needs to get themselves.
I know it's not the traditional thought when thinking of a DBA; however, the best DBAs I've ever worked with or had work under me where these types.