> I didn't call him childish.
I mean, you did though.
> You sound like a child.
There's no daylight between this and calling them childish. But I fully acknowledge they were also at fault, particularly the thing about getting you fired, and the reason I didn't make any defense of or apology to you is that it didn't seem to be getting under your skin.
I would say that response fails to demonstrate maturity, and wasn't an appropriate response to your question. You don't have to take the bait. Two wrongs don't make a right, you shouldn't respond to a bad comment with another bad comment, etc.
If someone isn't giving you something substantial to respond to, you can choose not to respond rather than responding inappropriately.