I hear you. No deep frying.
I'd been using it for saute on broccoli, spinach, kale, etc.
I've been led to believe I'm very healthy or horribly not because of this.
It's not a black or white issue. It's a "what's the BEST choice" issue. Long story short is that the second heat is introduced, you begin (slowly at first and then gradually faster) denaturing the healthy characteristics of the oil and producing free radicals which are damaging to our bodies. It's not the worst thing in the world to cook with, but the point is there are better heat resistant options to cook with, from a nutritional standpoint, such as coconut oil or Mac nut oil, or even cooking with pure lard/bacon fat/etc.
I personally keep my cooking oils separate from my dressings or dietary oils for a reason. EVOO is such an amazing oil in its raw unprocessed uncooked form, I prefer to savor every bit of it in its purest form so I ensure I'm getting all available benefits.