...but you realize that in the real world, you're better off kicking to low-line targets, right?

Of course, do as your instructor says...

Please define for me how this "real world" differs from full contact sparring.

There's two kinds of stretch - passive and active.

Passive stretch is when you hoist your leg on top of your partner and they lift it up - so you don't use your muscles.

Active is when you can take your limb through a range of motion using your muscles and no outside influence.

One of the major things that decides how high your kicks go under your own steam is actually your core strength. So your abs, back muscles, hip flexors, lats, obliques, etc.

One basic training that helps to build core strengh and kicking is to have two people stand facing. Hold out a kick (say a side thrust kick) at a low level like the knee - but don't touch your partner, just use them as a target - and count up to 10. Switch and let your partner do the same. Then do a middle level kick (gut) and then as high as you can go with good form. (If you don't have a training partner handy - aim at a chair)

Work your way up from a count of 10 to a count of 30. Work all your major kicks (front, thrust, roundhouse)

So the first step is getting the strength to hold your technique out at full extension - then you'll need to train moving and striking a target (like a focus mitt) to coordinate your new strength with your balance and timing.

Then go back to your partner sets and see if you can pull off higher kicks.

i assume he means that you dont have time to stretch in real world situations, + low line are less risky, shortest possible distance from target, and are just harder to read by non ma's.

all respect, burby