I wish I knew how to make animations like those sewing machine gifs everyone likes to post on Reddit. This would be much easier to explain. /u/khitsule is correct, but doesn't explain why.

There's more to the mechanics than that gif shows: What really happens is that the needle pushes the thread down through the fabric, and then rises up a bit (probably 2mm for a home machine). The thread is left behind, hopefully with some friction from the fabric, and creates a loop for the hook to grab. (That distance of needle-rise to hook grab is called the "drop" in industry terms.)

Okay, I tried with a quick mockup: Needle fully down. Then, needle rises up a bit. You can see when I pull the needle out a little, it leaves a thread loop. THAT is what the hook grabs. Gotta have that loop, or the hook misses it, and you have a skipped stitch.

You've heard of machine "timing"? In this case, it would be hook/needle timing: The machine is tuned to have the needle rise a certain distance so there's a loop for the hook to grab, but not TOO much, because that would cause other problems (that I won't get into here). But, I hope it makes sense that with straight-stitch, you want the right-sized thread loop for the hook to grab: That happens at a perfect time in the cycle, when the thread loop is right-sized for the hook to grab it.

But you're using a zig-zag stitch. What's different? The machine is timed for straight-stitch, so the right side of your zig-zag happens too early, and the left side happens too late. That is why your skipped stitches are always on the same side of the zig-zag pattern. It's tuned for "average", and zig-zag is not average.

But wait! There's more! /u/khitsule mentioned needles. Ball-point needles are designed to sew without shredding fibers in your fabric, because the ball-point goes right or left, instead of through a given fabric strand. Well that's cool and all, but a needle with a round tip isn't piercing fabric like a sharp needle, so it's pushing the needle/thread down with the fabric, which immediately bounces back up when the needle moves upward. Which means no thread loop for the hook to grab, so you get skipped stitches. (Industry term is "flagging", but I won't bore you with that).

Sorry for the TMI, just a bored industrial sewing mechanic, lol.