I believe what he was getting at is as an adult, you should be able to realize that a website on the internet is just that--and have the ability to take it with a grain of salt without being highly offended / outraged.

I don't think the intention was to say everyone on Twitter are adults--in fact it's the complete opposite of that. It's a platform where you can get both the best and the worst from all walks of life across the world. Sometimes there will be jerks and people who are the polar opposite ideologically to what you agree with.