I'm also in Chicago and have done a similar analysis. But I'd argue there are two main reasons for the per-month costs for owning are cheaper than for renting:
- Illinois is broke and is going to increase real estate taxes every year for the foreseeable future. So while you can also sell to escape the tax bill, the value will just drop to compensate. - There are many fixed costs to buying a place that aren't reflected in the monthly bills. Such as closing costs on both the purchase and sale (including chicago's lovely transfer stamp tax, realtor commissions, etc).
Also keep in mind how many high-rise condo buildings are going up right now. This can only be bad for prices of "old" condos around the city.
Basically, because it's much easier (in time and money) to switch leases than it is to go through the hassle of buying and selling a house. There are some markets where owning is cheaper, and some markets where renting is cheaper.
Money-wise, you're no longer throwing it away on rent, but paying down a mortgage that eventually is paid off entirely.
On top of that, you're also no longer racing against the end of the rent contract, and can wait a bit - or move earlier - to find a new place you really like.
The turning point for me was, here in Chicago, when I was renting and my dad sent me some properties with the costs laid out: These places were significantly nicer, and the mortgage cost per month was ~60% what I was paying in rent.