using equity to buy properties, worth the higher mortgage payment

After reading Brandon Turners book "rental property investing", I'm intrigued by the strategy of buying properties with equity(through home equity loans or lines of credit) you already have on current properties. BUT I just realized that once you take the equity out you will now have a higher mortgage payment and basically erase all the progress you've made on paying off that property... unless I'm missing something?

Here's my math on my Chicago Suburban home that I'm thinking about taking the equity out of:

$450K assessed value

$230K left on loan, 20 years left on loan at 2.5%. current monthly mortgage $2,050 with taxes/ins/int

=$220K equity

If I take out $130K to buy a new property, leaving 20% (90K) in equity to avoid PMI, I would now be paying off a $360K loan on the house and my mortgage amount would go up to $2,700/month. This is a $700 a month increase in mortgage payment.

If doing this on a rental property the increase in mortgage might make me negative cash flow due to the rental income not covering the mortgage.... so how can you build wealth or make a profit by using this method of buying houses with equity on your existing properties?