We have 5 bedrooms with 15A arc suppression circuit breakers. In 2 bedrooms sometimes when we turn off the ceiling fan, it pops the breaker in the basement circuit panel. Is this normal because it sometimes has an inductive current kick due to the part of the ac cycle when the switch is turned off?

No it is not normal for any breaker including arc fault and GCFI to pop just because you switched something off. However, arc fault and GFCI are more touchy than a regular breaker. Before considering replacing the breaker tcheck the panel and all outlet boxes for tight connections. Also go to the panel and switch the black wire from one arc fault to another arc fault to see if the problem travels to the new room, if it does replace the breaker. If the problem remains in the room even though you are now connected to a new breaker then the fan itself has an issue.

The switch is faulty. Change the switch will stop the Arc Fault breaker from tripping.

Thank you for your response. I will try replacing the switch first.

I guess you mean switch(s) since this problem poped up in two different rooms. These aren't remote control variable speed fan switches are they?