In some regards, he has a point though
At A-Level, I studied Double Maths, Physics, Chemistry, General Studies.
My performance in General Studies (the exam I took involved 3 hours of solid essay-writing) suffered dramatically because I just couldn't write for that length of time. I was crippled with cramp for the last hour of the exam - I got to write only a fraction of what I wanted to, and my grade undoubtedly suffered as a result.
The people who were studying English Lit, History etc, who were used to writing for that period of time, had a huge advantage over someone who was used to scrawling equations and formulae, and very little prose.
Granted, there is an art to essay-planning when you are hand-writing an essay, but I don't see how that is actually a relevant skill these days. If you've got 3 hours to produce some content, it's the quality of the end result that matters, not how you got there. With a computer you could effectively spend 2 hours vomiting ideas all over a page, and an hour tidying it up, and without the constraints you have to set at the outset of a hand-written essay, you may arguably end up with a better outcome.
Anyway, fast-forward 4 years to my University Finals, where, in an Objected Oriented Programming module, I found myself having to write about 20 sides of code on A4 using pen and paper. It turns out I got marked down for using ditto marks to speed the job up and avoid the cramp that had crippled me in the past. Bonkers. If I'd been on a computer, I'd have copy/pasted a bunch of lines and made the relevant changes. Instead of marking me based on what I knew and what I could produce in terms of working code, I was marked on the basis of being able to write it using pen and paper, which is a completely meaningless exercise.
Similarly, when was the last time, at work, I was appraised on something handwritten? Never.
I have to say, BYOD for exams is a bonkers concept though.