I'm asking to borrow an amount less than the total equity in my home. Why isn't this a slam dunk?

So I'd talk to a banker but I'm effing busy as eff during the day.

Backstory: Took out a GreenSky loan for some basement work to the tune of $13,000 @ 18% APR. It was quick to do and it's been interest free for the first year. Slowly over the year I whittled that down to $12,000. (I can do more but I'm paranoid about dipping into my 6 month emergency fund, plus I've had to pay $300/mo tuition for my daughters all day kindergarten)

Depending on who you talk to my house is valued at anywhere from $200,000 to $225,000.

The current amount left to pay on my house is $160,000 so $40,000 of pure unadulterated equity in what is also a hot real estate market.

So I figured the bank that I've had a super long history with (Nothing more than checking, savings, credit card but long history regardless) would beg me to borrow money from them.

So I apply online and a week later get a rejection letter back saying my debt to income ratio is too much.

Why the hell are they concerned about that?

If I default on the full $12,000 they get a house worth $200,000 easy. Sure they have to pay $160,000 on it but in the end that's a $27,000 profit.

#1 What am I missing here? Why does the bank care about my debt -> income ratio with the amount of equity in my home being substantially more than the amount I'm asking for?

#2 If I'm going to have this D -> I ratio cloud over my head what's a good alternative for getting something to reduce this interest rate? Prosper and Lending Club can cut it in half but the term lengths are too short for my liking bumping up the monthly payment.

Tell me some good news reddit. I'm not freaking out yet, but I am getting paranoid over this just a touch.

Thank you!!