It's when you don't treat it that way that you rationalize negative cash flow as investing.

If you're not concerned about making money, then rationalize the number your just came up with.  

@Jay Hinrichs My rules for REI:1 - Never lose money on purpose2 - Never rationalize Rule #1

You will need to deal with tenant deposits, outstanding invoices, possibly tax and insurance pro-rations, rent pro-ration, transfer of utilities and any service contracts, etc.

When you let non-math and/or emotions influence you investment decisions, you should be prepared to accept the low to average returns...and then rationalize that they are the norm and not low to average. 

Depending on what capital you may get from your settlement and how you need to rationalize what you do with it, you could look into an FHA loan and pay as little as 3.5% down.

While I am leaning toward the “Pro” contingent, (logical arguments abound) I do think there is a reason we sometimes get a gut check like the one you are having. 100% of the times I rationalized myself into ignoring that gut check I have regretted it.

Is there a way to have a rational discussion with them about the issue and try to work with them? 

There is are some loans that just look at debt service ration

I don't see a reason why an individual couldn't do likewise borrowing against a secured asset, but not everything about REI is strictly rational, and for all I know there could be regulatory restrictions against even trying this sort of thing.