You will not burn up your transmission any faster using M than using D, with one possible exception: if you use it to downshift for engine braking.
I have a 2011 with the V6 and use M for engine braking, but I also keep that in mind. It has 147,ooo+ miles on the original transmission.
What you need to know about your 6-speed is that it shifts automatically no matter what. All you're doing when you put it in M mode is sending a shift request, not a command, to the BCM and/or TCM, which then uses a LUT (look-up table) to determine if it will allow the request or deny it. When a request is allowed, the transmission shifts the same as it would in D, except that you are the one who made a request rather than the TCM.
Also, as you are probably aware but which your 'friends' may not be, is that it is not a DCT - dual-clutch transmission. It is an automatic that allows user input through a switch (or switches in earlier models with the steering wheel-mounted buttons). It uses TM - torque management - to reduce the amount of throttle being applied, shifts to the next gear, then reapplies the throttle. It can adjust the throttle because it is DBW - drive by wire - and so the throttle plate is controlled by an electric motor, not a physical cable as in years gone by.