I wish I could see what is happening.
It sounds frustrating all right. From what you say it sounds like you are doing it right. I just tried something that produced your effect. Are you sure you are going into the stitch loop itself that is on the left needle? I tried knitting between the stitch loops and it did what you say.
You insert your right hand needle (RHN) into the first loop on the left hand needle (LHN) going into the loop on the LHN from the left of it moving toward the tip of the LHN. Using the skein yarn, draw up a loop and pull it to the front, then take the first loop off the LHN.
I knit Continental too. As long as you are going into the loop on the LHN and drawing up a new stitch loop onto the RHN you should at least be making stitches. They could be backwards or something if you made other mistakes, but you should have a stitch.