...How childish is for someone in an executive position to start whining on Medium in the name of the company about something as serious as legal issues? Did they start hiring 12 year olds after the recent mass exodus?
It's not childish. It can easily be a strategy to convince (retail) investors and users that Coinbase is in the right thus they shouldn't worry about this going too bad for them.
But surely there's a more formal and professional way of handling a serious subject than rambling on a blogging platform?
It is charitable to call it childish. It is unprofessional. And it indicates a culture of "the rules don't apply to us because we are so cool".
Again, the reasoning behind it is likely for convincing investors/users they are in the right and as far as I can tell it is working - I see a lot of tweets of people buying Coinbase's response and raging against the SEC and people like balajis retweeting them.
As a customer of Coinbase for a long time (since 2013), I'm happy they tell the public what's going on, even if it's bad or good. Their customer support is abysmal, so any updates from their own back office is good to me.