can i terminate a lease at the end of the lease term?

[Jasmine NA]

location: San Jose, California

My tenant's lease is up on May 31st and I would like to terminate his lease / to not continue another term, although his rent is up to date and his job is not impacted by covid.

I gave him the termination notice and he said he would take legal action against me because I should not terminate the lease due to covid. It looks like they will have to apply for eviction protection? such as https://www.cdc.gov/coronaviru... And the protection ends at the end of June 2021?

I looked up online and it seems like all the advise are for "eviction". I am not quite sure if this falls into the eviction category. And he has always paid rent and did not lose his job. I just have other personal issues with him. Can i still tell him to leave by the end of May?

Thank you :)