Some literary agents are also authors, but they have another literary agent to represent their books. Why they don't represent their own books directly?
Agents understand the value of an agent. You can't agent your own work if you want a good agent, even if you're a good agent for everyone else.
Agenting requires distance and perspective that aren't possible if you're also the writer.
Agents who agent themselves will tell you I'm wrong. Their editors will tell you I'm right.