When combining butter with oil, the solids in the butter (which is what burns) will burn well before the oil is at proper sautéing temperature, especially if you're trying to pan sear or caramelize something. For proper sautéing, your oil should be at least at light smoke before you add the food to the pan. At that point the butter solids will probably have burnt. If it's a light saute where you're not looking to get too much color in the food, then that's fine; you can go with just straight up butter or with a butter/oil mix. If it's not a lighter saute, the butter will burn regardless of if it's combined with oil. There's two ways around this:
1.) Use clarified butter.
2.) Start with oil only, then add butter near the end or to baste with.