Why won't a fine-tip stylus work on my phones/tablet?

I've been using my tablet/phone for sketching with my finger for a long time. Over the last year or so, I've been trying to find a fine-tipped stylus to make drawing easier, as fingers are unwieldy and imprecise. I've purchased a few but none of them work with my Nexus 7, SGS2, LG G2, iPad, iPhone, etc. The styluses with the fat, rounded, mesh-like pencil eraser sized tips work, but they have the same problem as my finger: they are too fat to see exactly where the tip is touching the screen. Many styluses come with both ends, and I am left using the fat end every time. I've searched up and down for a reason but I've not been able to find any sort of explanation really at all. Can someone break down why the fat, pinky-like stylus tips work but the skinny, pen-like tips don't on (what appears to be) most touchscreens? Am I simply out of luck, or is there a screen/stylus combination that will work for me?