Why are men named John nicknamed Jack?

Brewer’s Dictionary of Names says that Jack comes from the diminutive form Jankin (“little John”). The Oxford English Dictionary also says that there is a strong case for this theory.

Jacques is Jack or Jacob, which is another name that's shortened to Jack. Nowadays Jack is used as a name in itself, though my friend's father was called Jack in about 1920 and actually had a brother called John as well. My Grandpa was called Harry and had a brother whose middle name was Harold, so certain pet names have been used as real ones for some time.
However (as it's relevant to Funtrivia) Terry is an English name in its own right, where Terence (also shortened to Terry) is from the Roman Terentius. Yes, names are one of my topics!