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.
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.
But surely there's a more formal and professional way of handling a serious subject than rambling on a blogging platform?