Having been an admin on a CS 1.6 server, and having occasionally visited other public servers, I can relate to your frustration.
In our clan, one guy spent hours practising to be an awpwhore. He got so good at no-scopes and headshots that even I got frustrated playing against him. Any server we went to, he was immediately accussed of hacking. It was only a matter of time until I was also accussed; though I certainly wasn't an awpwhore (I loathed the thought), I knew how to look and listen and that was often more than many noobs could understand ("How did you hear me coming? Hacker!").
On the other hand, as an admin for a server, we often had people hacking, as well as people whining and complaining that the good players were hacking. It can often be difficult to tell the difference; though some hacks are obvious (e.g. the aimbot that suddenly points towards a wall and scores a headshot on the other side), others are nearly indistinguishable from regular play. I have no doubt that we sometimes banned people who were just unbelievably good. Since we had a reputation for being good players ourselves, we often attracted other good players. This meant both that it was difficult to tell the good from the hackers, but also that we expected this and required substantial proof before banning someone.
To make matters worse, the cheaters are often more vocal than the good guys. We had more than one person using the obvious aimbots that bitched and whined when we banned them. They peppered our forums with insults and demands to be unbanned (why do so many 12 year olds think that name-calling will encourage people to be nice to them?). They accused us of banning good players, etc.
So, while it's entirely possible that the admin who banned you is really inexperienced and can't tell the difference, it's also possible that you are good enough -- and so are the cheaters -- that it's hard to tell the difference.
In either case, while it's frustrating to be continually be banned from servers, appreciate the fact that your skills are unbelievable. Your best bet is to find a good clan to become friends with -- amateur clans will be the first to ban you, but good clans will befriend you quickly when they see your skills and they won't be quick to accuse you of hacking. Once you find the trust of a group, you can rest assured they won't be banning you, even if some loud-mouthed kid accuses you. You can usually tell the good admins apart fairly easily -- they'll ignore the loud-mouthed accuser for awhile, then finally come out saying, "He's not hacking, STFU." Avoid the ones that are quick to ban anybody who speaks up, mentions hacking, or otherwise seems more than happy to exercise his artificial power.
I apologise I was just frustrated. I'm also new here 
