Introverted people as a group are as diverse as any other group of people. The only thing that sets introverted people apart from extraverted people is what they do following social interactions: introverted people look inwards to recharge while extraverts look outwards. In short, if spending time in a group makes you feel tired and you seek time on your own to recharge, that means you're introverted. If spending time in a group makes you feel dynamic and full of energy, that means you're extraverted. Everyone is somewhere on a spectrum between those two states.
Being an introvert in a society that values social interaction so highly is difficult - take a startup accelerator with social events practically every night as an example and it's obvious why. Being the person who goes home early and gets labelled 'shy' or 'antisocial' puts you at a great disadvantage when really you're just genetically predisposed to feeling better spending time on your own (or in smaller groups).
There is no reason whatsoever why an introverted person wouldn't happily use Wordpress/Tumblr/Jekyll/whatever for their blog. What you are catering for (eg "people who want to blog anonymously") is something else entirely.
Having just deployed this app up last week, I am experimenting with different ways to describe it. I was unsure of the "introvert" tact to begin with, and am now certain it is not the best choice.
Rather than misunderstanding introversion (as you claim I do simply from reading an experimental tag line for a web app), it is more likely that I failed at capturing the essence of the product in the tag line. There is plenty of successful marketing copy that uses words differently than a thoughtful definition would dictate.
I think the wise choice is to remove both notions of blogging and introversion from the description, and focus more on the process of writing. My goal is to create a place to write on the web that feels offstage from the large social networks that I believe extroverts thrive on.