The Kohathites had an important role: to carry many of the holy things from the tabernacle when the Israelites were moving between camps, but without actually touching them directly (see Numbers 4).
One of that clan, Korah, wanted more. He stirred up a couple of his mates and 250 other community leaders in an attempt to get more of a ministry than God had allocated. His method: put Moses in his place (as they saw it):
You have gone too far! The whole community is holy,every one of them, and the Lord is with them. Why then do you set yourselves above the Lord’s assembly?
It was a direct challenge of the form “Did God really say …?” Moses’ answer was straight to the point:
The man the Lord chooses will be the one who is holy. You Levites have gone too far! … Isn’t it enough for you that the God of Israel has separated you …?
And God backed up Moses.
Korah and his two friends were destroyed, but only after God warned everyone to get away from them. The 250 community leaders were consumed by fire as they tried to offer incense to God (this was a role reserved for a few).
Reading through this whole account reminds me of pastors who just try to do God’s will and get nothing but grumbling from their congregations. People should count themselves fortunate indeed that Jesus has already died for their grumbling as well as their other sins.