One more tip – people remember stories that trigger their emotions.

Avoid the cash offer stuff, and saying quick closing in letters, use emotion, people really do respond well to it.

Is this an emotional and preference thing or a true need?

We have simple form letter that says "the information you provided does not meet the requirements for an Emotional Support Animal".FWIW, you could also change your no-pet policy.  

We keep it professional and try not to get emotional about it.

Also this emotional pressure is really common with high pressure sales environments, which is often the case with large wholesaling organizations. 

+95% of agents only have experience dealing with owner-occupied transactions - which are mostly EMOTIONAL decision based.You can ID these types of agents easily by asking them:1) If they are RE investors themselves.

This is the best way to eliminate gut or emotional decision making.

Also, come resale time, the duplex would have a proven track record of producing income and has definable value, whereas a single family home is largely dependent on current market conditions and home buyer emotions and buyer pool at that given time

Document everything sticking to the basic facts, try to leave emotion out of it.