It's difficult to say. You haven't given us very much information to go on. You say that you haven't used any cheating software, but the list of programs that are considered bannable covers more than simple scripting or botting software. Here's a list of allowed and not allowed third party programs that Wuks put together to give you an idea of the sorts of things that can get people in trouble.
With that in mind, let me ask you some questions. Is your computer a private computer, or do you share it with other friends/family members? Does you allow anyone else to access the internet, download applications or install programs on your computer? Have you ever let anyone else play League on your computer? Not necessarily playing on your account, but accessing the League client to play on any account? Have you ever accessed your League account from someone else's computer? Have you ever accessed your League account from an internet cafe or from a dodgy, unsecured internet connection? Have you ever used any type of client modifications or customized skins? Do you use any form of macros for casting abilities? Do you use a specialized gaming mouse or keyboard?
Lots of questions, I know. But I ask them for a reason. Answering yes to any one of them could potentially have led to this ban. Example: If you let a friend use your computer to play on his/her account and they loaded a quick scripting program without your knowledge, the way it was explained to me, it becomes associated with the client. And the next time you play on your account from that client it then flags your account in the server for third party applications, even if you aren't actively running it. Example: If you run a custom skin from one of the banned programs. That software is usually banned because of additional functions that the platform contains, that would give an unfair advantage to the player, things like timers. Even if you only use it for the skins, and never access the other functions, your account will still be flagged and banned. Example: You play League at a friend of a friend's house. And that friend of a friend is a dirty, rotten cheater who has every script, hack and cheat known to man hidden somewhere on his computer. As soon as you open your account through his flagged client, you get flagged as well, even if you didn't know about them or try to use them. Example: Macros. You decide to make it more efficient and bind multiple individual keystrokes of a combo play together. You've always wanted to do Riven's fast combo just like BoxBox and now you can. Except using macros like that is very much so not allowed. Example: Your dad uses your computer and is fond of clicking on every flashing ad because he doesn't realize that it's not safe to do so. Who knows what he has downloaded on your computer without your knowledge over the years!
So, now that I've asked you some questions, and given you a bit of an idea of what sorts of things that might seem pretty harmless but can end up getting you in considerable trouble, I'll explain a bit about why Support doesn't tell you exactly what caused the suspension. There's a small percentage of people who never can figure out why they were banned, even with some helpful ideas and a bit of poking. Then there is just a slightly larger percentage of people who were cheating and didn't realize that it was considered cheating. And then you have all those people who were cheating, and knew darn well that they were cheating. Some of those are the users, others are the designers. And the reason why Support doesn't tell all players how they were caught, and what specifically they were caught with and on what day, is because that would give all that information to the designers. The designers would know exactly how their cheats were discovered, and they would simply make them harder to detect.
So, to keep from making more work for themselves, Riot's policy is to inform players of the category, but not to reveal the specifics.