BRRRR refinance question

[CJ Witmer]

Ok, I've done a lot of reading here on BP and I have some sort of mental block because the refi part is just not sinking in to me. It seems like I'm just robbing Peter to pay Paul? Can someone explain this to me like I'm a second grader? If I buy a duplex for $60k ($12k down and $48k financed) and I put $20k into it and it appraises for $115k, that's obviously a good thing. My total investment is $80k. Using 70% LTV, I could theoretically get $80,500 back. So if I refinance, it seems to me, I'm up $500. I'm refinancing $80,500 to pay off my original $80k, which sounds dumb. Obviously folks are using it and it's working, it's just not sinking through my thick skull on how it works. Can someone help and explain it so I can comprehend?