Do not threaten the tenant but provide her legal written notice, per your states guidelines. 

If I threatened your professional worth, I apologize.  

From there the conversation was basically him threatening me or trying to scare me that "if I was afraid to pay the fee" I could walk away.

9 times out of 10 threatening court action is just that , a threat.

The seller is threatening to take our earnest money deposit when we tried to cancel during the inspection period. 

Generally, if amount of damage is greater than the amount of the security deposit, I'd threaten a lawsuit. 

The longer your tree hangs over the fence, threatening your neighbour's house, the greater the risk to you (you will be liable for damages if you do not take timely action to remove the tree (threat)).In the end, your insurer will re-imburse you the agreed amount minus your deductible.  

Zip is fine for market analysis, but the address really threatens his position

The answer is no,plain and simple.If he wants to run a home based business so badly,he can buy his own house and use his own insurance and take his own chances with city code enforcement.This is a legal disaster waiting to happen if you allow it.Find better tenants if they threaten to move,you'll sleep easier at night.

But it seems harsh to threaten eviction for a long time tenant who has not caused any other issues otherwise, or is it?