Cash out refinance to pay down mortgage on personal residence

[Jason Kimery]

So we owned and lived in a house for 5 years. Last fall we bought a new one and turned the old one into a rental. The rental is worth 160000 and we owe 55000. 

While doing our taxes we realized that we won't ever surpass our standard deduction therefore won't really qualify to deduct mortgage interest on our personal residence. We obviously can deduct mortgage interest on the rental.  It seems like I should do a cash out refinance on the rental and pay down my personal mortgage? Is that crazy? It seems like a big savings but I might be missing something