1) Employers know what they need.
The whole concept of employability rests on the assumptions that employers know what they need. They get to dictate course content, curriculum design and careers advice. The reality is different. Both because recruiters aren't just one person and because recruiters aren't particularly well equipped to predict the future. So take it with a grain of salt next time someone tells you want employers want: For instance, in an employer survey 21.8% said an applicant's university was the most important point when reviewing them for a job, even though massive graduate recruiters like Penguin Random House and Ernst & Young have stopped looking at degrees completely.
At the same time, you will find that "being qualified" is apparently one of the top 10 things employers are looking for. On the same top 10 list, you will find "a degree", despite the fact that 65% of directors who employ recent graduates believes your "employability skills" are more important than anything you learn at your degree. So despite all of the influence employers have over Universities' employability strategies, don't necessarily trust the assumption of coherence and consistency in the demands of employers.
After all, what employer could have predicted that people putting multi-coloured plastic bricks together would go on and build the most powerful brand in the world, Lego.
2) People are unemployed because they are unemployable
By the logic of employability, you don't have a job because something is wrong with you. You do not live up to the requirements. You're not the kind of person they want to employ. You do not supply what the labour market demands. Quite obviously, that's stupid. The unemployment following the financial crisis wasn't because hordes of people all of the sudden forgot their employability skills. Rampant youth unemployment across Europe is not because Spanish or Greek youth isn't enough on LinkedIn or don't know time management. People are unemployed primarily because there are no jobs.
3) Everything in your life can make you more employable
As mentioned previously, companies don't just want good degrees or demonstrable skills. They want whole people. They want to see you have experience, understand your own motivations, be engaged in co-curricular activities and have a strong network. In short, they want your whole life. This obviously poses a dilemma for you as a student. Should you get rid of your old friends, and make some new friends who will better help your career progression? Should you change hobbies to something that will better help you demonstrate whatever core employability skill is on your Universities web site? Should you change your social media presence to look more like a CV? Change your dissertation topic to something less interesting, but more profit oriented? And if you did all of that, would it make you the whole person companies are looking for?
4) Employability is about what you do
Even though it's all about you - and your hobbies and your friendships and your feelings - no one can really pretend that your employability can actually be reduced to the individual. Even though Universities surely offer their employability services to all their students, they still say that you should "give yourself an edge over other graduates", as Sheffield Hallam says. According to my own University of Leeds, an entire third of the employability strategy is about competition: decide, plan and compete. So when they tell you that you can improve your own employability, remember you probably can't. Not if everyone else go to the same CV writing workshops. This is not to mention that 'teamwork' is often considered a core employability skill. You are expected to simultaneously teamwork with and compete against your course mates. You are only really employable if people around you are less employable than you.