1. She can't keep a secret
The number one rule about being a spy is being able to keep a secret. I mean, the whole industry is centered around that idea. Emily's number one secret is her true identity and more people know that than Clark Kent's alter ego.
People who know Emily's true identity: Jack Porter, Nolan Ross, Mason Treadwell, Aiden Mathis, Satoshi Takeda (dead), Tyler Barrol, Gordon Murphy (dead), Frank Stevens (dead), Amanda Clarke (dead), Ryan Huntley, Warden Stiles, Carol Miller, and Eli James!
2. Her personal life gets in the way of her missions
How long do you think you could keep your job if your personal drama kept making unexpected appearances in the office? Probably not very long. Emily has had jealous boyfriends, crazy parents, and even overbearing sidekicks get in the way of her mission. If even one of things came up during a mission, MI6 or the CIA would give Emily her walking papers.
3. She's too hot
One the basic attributes of being a spy is the ability remain unnoticed. Plain and simple, Emily is too hot to do this. Whenever Emily walks into a room, almost every man's gaze is instantly drawn to this blonde bombshell. How is a spy supposed to get her work done if every person is looking at her?
4. She gets too close to her targets
You can't let your personal feeling get in the way of the mission. Does a hunter get to know Bambi before mounting his trophy on the wall? During her mission Emily seduced Daniel, fell for the guy, and then couldn't pull the trigger. A true spy would line up their sights and then rip the fragile psyche of their prey to shreds (followed up with a victory martini).
5. She keeps a record of her exploits
Come on; do you really need to keep a detailed account of how you are systematically ruining the lives of people? Did James Bond keep a journal? No. How about Jason Bourne. Nope. This is basically a box of evidence that could send you to prison waiting to be found. What kind of master spy leaves a paper trail anyway?