Incase you don't like videos or you still don't get what the problem is, here is my attempt of describing the problem.
I'm Having difficulty setting up my front derailer. I've had the bike for a while haven't changed any of the parts, but I had just ignored the issue and never switched to the gears that had problems. Now I'd like to fix it. By the way the gear system is Shimano, don't know the particular model. It says SIS Topswing Shimano on the gears, and my bike is a Sorrento Diamondback 21-speed mountain bike.
So when the front gear is in the lowest gear I set it up so that the chain is just far enough away from the derailer that it doesn't hit it when you pedal. However if you try to switch from the second gear to the lowest gear it won't switch gears. If I adjust it at all so that it will switch then the chain will clang against the derailer when I pedal.
Rans Enduro Sport, Hase Kettweisel Tandem, Merin Bear Valley beater bike
I think that I could train a chimpanzee to adjust rar derailleurs but fronts are quite a bit more difficult.
Park Tool has a good set of step-by-step instructions on their website. Pull it up, disconnect your shift cable and start from the very begtinning as if you were installing it for the first time. Be VERY particular about the position of the derailleur on the seat tube. Often, if that's off by even what looks like a trivial amount, that's the problem. Be sure to do all of the steps in order because each step can affect the subsequent adjustments.
+1 on checking out Parktool's website for front derailluer adjustment.
Ideally, when the chain is in the small chainring up front and your largest(lowest) cog in the rear, you should have a 1mm gap between the cage and chain. Unfortunately, due to the level of components, this does not always lead to a clean shift going from the middle to small chainring. In this case, you may need to loosen the low limit screw, so the derailleur returns further inwards. The angle of the cage and height of the cage, could also possibly need to be adjusted for optimal shifting. The angle is more difficult to instruct, but for height the lower part of the FD cage should just barely clear the teeth on the big ring(1-2mm gap). You can check the height by pulling the cage out until the outer cage plate is just over the big chainring - rotate the crank fully around and check the teeth in relation to the crank(you will observe that some teeth come closer to the cage than others).
You didn't show or mention where the chain was on the rear cogs in the video - if it is in the highest gear, the shift from middle to low up front will be more difficult.
I would add some more, but I have to head out...hope you get your shifting sorted out.
Your FD cable isn't tight enough. When you try to go from middle to small the cable needs to retract and pull the FD down, bringing the chain with it.
I've had this. When installing or adjusting, tighten the cable as much as you can when it is in the lowest position. Then, when the chain is big front / smallest back, use the limit screw to move the derailleur just outside the chain so as not to rub anywhere. When on the small front/largest back, set the screw so it stops just inside (frame side) the chain. Cable tension is all that positions it in the middle so it needs to be right. Use the barrel adjusters at the shifter to tension just so.