You do push the pen. Otherwise how would you write an O? like ()? Similarly there are upward strokes in h, b, d, k, m, n, r...
I would say that cursive ("joined up handwriting" as I know it) prefers downward strokes, and I don't think it ever begins a letter with an upward stroke.
That was a bad idea. Much better: graphics8.nytimes.com/images/2009/09/08/opinion/OPED-WRITING.1.pdf, briem.net, italic-handwriting.org, studioarts.net/calligraphy/italic/hwlesson.html, BFHhandwriting.com, handwritingsuccess.com, Lexercise.com, HandwritingThatWorks.com, freehandwriting.net/educational.html
You pull it on the upward strokes too. Have you used a fountain pen for long periods of time? The nib acts as a spring (in fact it's called a "feder" in German, which coincidentally can mean "spring" though it also means "feather" which, of course, is the sense in which it is used) if you push on it. Little kids learn with a special kid's pen which has a very strong nib because they tend to push down hard and to push on the pen.
I don't know if they still require it, but as of 5 years ago my kid was still required to do his schoolwork with a fountain pen (until grade 8).
I would say that cursive ("joined up handwriting" as I know it) prefers downward strokes, and I don't think it ever begins a letter with an upward stroke.