I dont understand the top lane

In my 4 or 5 years of playing League of Legends I almost never touched this lane, mainly because I didnt feel attached to 2 bulky bruisers battling it out up there but this season I decided to give it try and made another account to play top and jungle mainly.

Last game I was Irelia top vs Kayle. First thing I did was to draw a game plan in my head, my thougts were like this: Kayle is very weak early and Irelia is good at trading, especially with the passive, so I'm gonna freeze the lane close to my tower and punish her whenever she overextends or throws abilities to CS. Said and done, she started missplaying by autoing the first wave, allowing for a freeze on my side. Close to min 3 I killed her because she was way too overextended and I had my passive stacked. From that point onwards I continued the freeze denying her CS and snowballing my advantage. At min 7 I killed her again because I was lvl 6 and she was still 5 so easy kill with my ulti. Ok up to this point everything is good and it all worked as expected. Problem comes at min 9, where I missed an E and decided to take the trade anyway because I thought my 2 kill lead, lvl lead and item lead would be enough to suffice for that missed ability, but I was wrong and I got killed. At this point Kayle was 1/2 and I was 2/1, for some reason all the lead I had built up to that point just crumbled in an instant, when I came back to lane she was the same lvl as me, she had closed the gap in CS and now she could even smash me in a 1vs1.

Besides that bad trade I took at min 9, I dont understand what I did wrong, its not possible that if you build and advantage for almost 10 minutes straight denying your oponent and mess up once, all that effort you did is gone and worthless and suddenly your enemy that couldnt even walk up to farm up to that point just rolls you out of the lane from that moment onwards.