A companion should be many things. Loyal, intelligent, relatable, adventurous. Most importantly, they should have their own life outside of their time with the Doctor. The best example of this was the Ponds, who broke the trend established by previous characters by having their own lives completely independent of their time on the TARDIS. The problem with Clara is that she doesn't have a reason for existing independent of the Doctor. She even calls herself the girl who saved the Doctor. Now that she's saved him, Clara doesn't really have a reason for being. Moreover, the constant teasing of her departure from the show has really started to get on everyone's nerves. Like the Ponds before her, Clara has expressed a desire to have her own life independent of the Doctor. The Ponds managed to keep their lives on Earth largely separate from their time on the TARDIS, and the few times those lives intersected were all the richer for it. But Clara seems to have no problem involving the Doctor in her personal and working life, whether it be alien death machines rocking up at her school or taking students on trips to the moon. Not only has she already died twice and decided that she wanted to be independent of the Doctor on half a dozen occasions, but she's also supposedly left the show on at least two separate occasions before Jenna Coleman changed her mind and decide to stay on for another series.