I don't really buy this argument that you can rent and pay $1000/month, or you can buy an equivalent home and pay $1000/month, but now you can deduct interest rate and build equity.

Landlords can also deduct their interest expenses and so they benefit from leverage too (meaning they don't want to build up equity).

In a reasonably efficient market, this means that the equivalent cost of homeownership would be higher than rent, to offset these things (the rate at which you're paying down the principal, and the deductability of interest rate expenses). This is obviously a very simplified argument, and there's a lot of other factors going into this.