It's a game ban; cheats aren't necessary for that.
There are several possible reasons.

Before you ask:
x) No, nobody here can tell you the exact reason in your case.
x) No, the ban is permanent and cannot be lifted.

引用自 yuxusuzluq yox500+：

I don't understand why I was banned, because I didn't play with any third-party programs. I played in normal mode, and people who don't know how to play probably sent complaints.

The funny thing about a game ban, is you don’t have to cheat to get one

引用自 yuxusuzluq yox500+：

my account was given a VAC ban by mistake
I don't understand why I was banned, because I didn't play with any third-party programs. I played in normal mode, and people who don't know how to play probably sent complaints.

1 game ban on record | Info
1 day(s) since last ban

The only mistakes you making, is coming to a community only forum to appeal a permanent ban and also that you thinking that you have a vacban, while you have a gameban, irrelevant what it says in game.

So go to your profile and click on the info button next to your gameban.