Or HaChaim on Numbers 12:11/אור החיים על במדבר י״ב:י״א

1 בי אדני אל נא תשת עלינו תטאת, "please my lord, do not lay a sin upon us, etc." It is clear from Aaron's words that he believed Moses had felt slighted by their comments. This is why he pleaded with him to forgive them their sin. It appears that Aaron reasoned that Moses would view himself as a חכם, merely a wise man who is legally entitled to waive his honour so that those who slighted it could be forgiven. Aaron presumed that forgiveness by Moses would result in the Tzoraat being cured. Accordingly, Aaron said: "though you have been offended by our words so much that we have been punished on their account, now that we have suffered the punishment please forgive us so that we will no longer be guilty of this sin." The truth of the matter was that Moses had not felt offended at all. The Torah demonstrated this by writing how humble a person Moses was specifically at this juncture. This was to show that Aaron had been wrong in his whole assumption.

2The reason why Miriam and Aaron were punished is twofold. 1) Moses could not be treated merely as a חכם, a sage, but had to be accorded the status of a king. (This is based on Deut. 33,5 that Moses was king amongst the people called Yeshurun). A king is not allowed to waive the honour due him; therefore Moses could not have forgiven the insult even if he had felt like doing so. Moreover, this may even have been what G'd alluded to when He described Moses as His servant in verse 8. According to the Talmud in Shavuot 47 the king's servant is to be accorded a status similar to that of the king himself. Seeing that Moses was the servant of the King of Kings, he too was to be accorded Royal status.

32) I have already explained that G'd was very concerned at the fact that Miriam and Aaron had suspected their brother of serious wrongdoing. If G'd had not rebuked and disciplined them it would have given them the impression that G'd Himself condoned and agreed with their criticism of Moses. This is why G'd had to punish them even though Moses had not even felt offended. Moses was justified in not praying immediately that the Tzoraat be removed seeing he had not been its cause, as he had not even felt slighted by Miriam and Aaron's remarks. Had the matter been up to Moses he would not have had to pray. All he would have had to do would be to forgive (if he had felt insulted) and the Tzoraat would have disappeared. Under the circumstances, his prayer would not become effective until after seven days had elapsed. Clearly the punishment was due to either or both of the reasons we have mentioned. We cannot imagine how much more severe the punishment would have been if Moses had indeed felt offended by Miriam and Aaron's criticism of his conduct vis-a-vis Tzipporah.

4אשר נואלנו ואשר חטאנו, "for we have acted foolishly and have sinned." Both expressions refer to their error when comparing their level of prophecy to that of Moses. G'd's reaction had made it plain to them that the comparison of their prophetic powers to those of Moses had been foolish; the fact that they accused Moses of not having marital relations with his wife had been sinful.