There is a lot of misinformation going around on this subject, including on this website.
Tenants are often anxious to get all of their money back no matter how they have taken care of the apartment. They often have no idea about what their responsibilities are during the course of a tenancy, and they are happy to jump on the phrase "normal wear & tear" expecting that this will shift all responsibility to the landlord. Unfortunately, it seems that even many lawyers are not really knowledgeable about what this phrase means, and often give encouragement to tenants to try to escape their responsibilities with this excuse.
Your tenant is full of baloney in trying to make this excuse. I say this, not because I am a landlord myself, but because I have studied the matter and I know about it. The concept of "wear & tear" is just that: wearing out and deteriorating from age and being used up. It does not apply to lack of cleanliness and carelessness or neglect.
The concept is not vague and subjective, it is exact and specific, although too many tenant advocates and others who haven't given the matter a lot of thought, have written about it and given definitions which are not correct.
See:
https://forum.freeadvice.com/showthread.php?threadid=42675
