Setting aside any concept of who's "right" or "wrong", if I got an email like this from the MD of a customer, I'd share it with my team, we'd all laugh a bit, take a deep breath, and find a way to de-escalate the situation.

Similarly if I were buying product from a supplier and they made an immature joke I found hurtful, I would probably just ignore it. If it was a recurring problem maybe I'd say "I really didn't appreciate when you <xyz>'d, can we keep this focused on business in the future?" And if that didn't solve things, I'd see if someone else could be assigned to handle the account.

I hope those examples don't minimize what either side is feeling, but I have to say that I don't feel I've seen anything in this thread that gets my blood pumping. Dealing with difficult or rude people is part of the job and part of life.

Taking things personally, especially in business, is a _very_ expensive luxury. And if that isn't convincing enough, if you still feel angry about it in a month you can usually yell at them later. But if you escalate today and feel foolish about it later, it's a lot more difficult to mend the wounds.