Calhoun (rhetorically, with a dab of sarcasm) gave you the answer...
There IS one situation where fouls by both teams MAY or MAY NOT off-set.
That is when there is a change of possession during the down in which each team commits live ball fouls. If the team in final possession fouls following the COP, they are considered to have gained possession with "clean hands". Therefore, by rule, that team will have the first choice and MAY accept or decline A's foul. If they decline their opponent's foul they will retain possession, but the team NOT in possession will undoubtedly accept the team now in possession's foul. The team in possession will next snap the ball following enforcement of their foul. If the team in final possession accepts their opponent's foul, and the team not possession accepts the team in final possession's foul, we have a DOUBLE FOUL and will replay the down.
Finally, unsportsmanlike and non-player fouls CANNOT be off-set with an opponent's foul.