My child does this too sometimes, it’s sometimes a form of testing their own power over the world and sometimes odd humour .
If it’s obviously a deliberately false statement I tend to dismiss them with some form of “Don’t be silly” or “Poppycock”. Not arguing, but dismissing something as silly can be more effective.
My parenting philosophy is that to earn children’s trust, you must be truthful with them. Parents are also tasked with protecting children from too much pain. In practice, this means giving them the truth in a way they can process.
Tell them well in advance.
On the day let them hug the cat as it leaves. Tell them this will be the last time.
In the best case, they will be sad and angry. They might also be confused. Let them.
The above poster gives good advice.