How can I disprove a claim of retaliation?

Question Details:

My tenant gave me a legal letter regarding the repair of the dishwasher 6 days after his request for such repair. I thought I had 10 days for an item such as a dishwasher. The problem is that now if I evict him, he can claim retaliation? I believe that he did this knowing that I was going to have to move back into my residence (his rental). Can we still give the tenant a 60-day notice? Important Notice