To flap or not to flap?
You don't say which variant you're flying, but the C42B is perfectly capable of both taking off and landing with zero flaps on a reasonable-length runway. I've done it on several occasions with huge margin even for touch-and-gos on my home field's 1300 m asphalt runway. You do need to adjust the angle of attack (via pitch), but if you're flying the airspeed you'll basically be doing that anyway, so no big deal.

Extending flaps give you better flying characteristics at low airspeed, but increases drag. If you're flying the approach at reasonably high speed, then you likely don't particularly need the extra lift, and in fact it might even be detrimental especially once you're wheels on runway and trying to slow down. With flaps extended, you also need to monitor your airspeed more closely to make sure you aren't exceeding VFE.

On the flip (flap?) side, the C42 flaps lever manipulates the flaps directly -- it's just a cable going through the fuselage. Any time you're handling the lever, you are fighting directly against the airflow around the wing, with no help from e.g. elevator trim, let alone hydraulics or even electrics. I know that the effects of this came as a bit of a surprise for me the first few times I retracted flaps in flight; it's very easy to end up with a rough flaps retraction if you aren't prepared for the force involved.

You're supposed to be flying the airplane all the way to the ground, and only bleed off the flying airspeed very late during the landing, in the flare when you should end up at stall speed with the wheels just barely above the runway.

It's possible that your instructor feels that the added complexity of also handling the flaps lever (and the resultant drag changes) simply may risk being overwhelming at first. It's not like there isn't already a lot going on during a standard traffic pattern coming in to land; there's airspeed, altitude, auxiliary pump, carb heat, scanning for traffic, radio communications, keeping good tabs on your position relative to the runway, lining up for final approach mind the wind, making sure your turns are coordinated, during crosswind landings the final turn to align the airplane (as opposed to the direction of travel) with the runway, ...

Your instructor likely has a plan for how to introduce the use of flaps during landing; you are most likely going to need them by the time you're doing short-field work, if not before. You also can, and should, discuss with your instructor anything where you don't feel that you understand the instructor's rationale. Asking strangers on the Internet for advice is fine, and can provide additional insight (which can be quite valuable!), but should never be a replacement for asking your instructor.


  high incident rate that involve overshooting runways


If you're too far along the runway to land safely, just go around and make another attempt. (Landing long is fine, just annoying if you need to taxi all the way back; overshooting the runway is not.) It's good practice for everything except the flare, braking and taxiing, and it's good practice for go-around procedures. I've made the decision to go around in situations that very likely were perfectly fixable (things like being too high on final, or drifting to the side while still a moderate distance out on final) but I am of the opinion that it's better to go around and do it right, than try to press on when things are stacking up against you, especially if you're new. With experience, you'll learn what can be fixed in-place and what truly warrants a go-around.

Just make sure you tell the instructor what you're doing. Crew resource management isn't a big focus in single-pilot light aircraft, since you'll mostly be flying by yourself and certainly a lot of the time without another pilot in the other seat, but I find it's a good idea to follow the general principles anyway.


  Additionally, it doesn't seem to prep you well for the 'real world'. I can't imagine telling your F.O on a 737 'Don't worry about flaps today, it's too much to think about' :D


I know you added a smiley, but it's no joking matter. Don't treat, or think of, the C42 like a commercial jetliner. Don't think learning to fly a C42 will allow you to just drop into the cockpit of a jetliner (even a realistically simulated one) and fly the latter. It isn't, it will never be, it won't, and the C42 handles quite differently from the big iron. That doesn't make the C42 any less "real world".