If you had been my child, I would have demanded that such an irresponsible teacher be fired.
It is the subjunctive mood, I suppose. Why every verb in the sentence in the past, but be is in the present?
Answer
Subjunctive tenses are a little more abstract with respect to time than indicative ones are. This is a good overview of usage: http://en.wikipedia.org/wiki/English_subjunctive
With the verb to be, past tense implies a condition known not to be the case, whereas present tense doesn’t imply that knowledge. For example:
If Abraham Lincoln were alive today, he probably wouldn’t be able to run for president.
Be he alive or be he dead, I’ll grind his bones to make my bread.
Attribution
Source : Link , Question Author : Graduate , Answer Author : BobRodes