Have you tried to find something?
Let me help you:
http://caniuse.com/#feat=namevalue-storage
http://stackoverflow.com/a/3220802/680786
In short: LocalStorage is supported by all browsers, has no security issues as cookies have, has much bigger storage limit, much more handy API and don't need to be send on each request.
Source? Not saying I agree or disagree, but a statement like that without any supporting arguments or discussion isn't particularly helpful.