Oh, poor THAC0. When people talk about older editions of D&D, and how the rules can be confusing, THACo is often dragged from its poor cupboard under the stairs and beaten viciously.
AD&D 2e is usually credited with the advent of THAC0, but shhhhh...lean close to your monitor because I want to whisper a secret...
THAC0 has always been there.
No, really, it's true. However, like other sorts of conditions you can have, people often don't think it exists until you give it a name. You just like to double check that the doors are locked at night 13 times before you go to bed (and get out of bed 5 more times just to make sure), until someone tells you it is an OCD, then suddenly you have OCD. So OD&D, Basic D&D, and AD&D 1e all had the THAC0, they just didn't know it.
I think the confusion around THAC0 is partly there because it begins to meddle with your sense of reality as soon as you read it. I mean just look at it. THAC0. "To Hit Armor Class Zero." Uhh, wait a second. Shouldn't it be THACZ?? Well that doesn't have quiet the ring to it.
One thing you may not have thought of is that there could be a THAC4, or THAC-3, because choosing 0 as the starting point was arbitrary, but intuitive (or maybe it just sounded better). The reason I say that THAC0 has always existed is because although older editions relied on presenting the full attack matrix, all THAC0 does is save space and make you, gentle reader, do the math yourself.
That's where the second problem comes in. But before I continue, I feel like we've gotten to know THAC0 a little better, so we can do away with formal titles. Lets call him Chad instead. Chad is just the personification of a simple algorithm. Where the confusion sets in is that we are dealing with opposites. In order to get rid of that big clunky attack matrix we just say, "Ok, Chad tells us that a 1st level fighter needs to roll 20 to hit an AC of 0." Easy, right? Now what happens if you (as the fighter) are fighting someone with an AC of 4? You subtract 4 from Chad, so you need to roll 16 or better. Why? Because remember that the higher the AC the worse it is and the easier it is for you to hit your opponent. Now, hah hah hah, here we go. What if, brace yourself now, you're a 5th level fighter and Chad tells you that you need 15 or better to hit AC 0, and you are attacking someone with AC-2. You need to roll 17 or higher. That's right! Remember, negative ACs are harder to hit. You add a negative AC to Chad, but you subtract a positive AC from Chad.
You see, the thing is that it is simple arithmetic. It confuses people because you subtract positive numbers but add negative numbers when normally if you add a negative to a positive you subtract. Hmmm, I'm not sure if that helped you or not. But don't blame Chad, because it isn't his fault. He's just a scapegoat because someone wanted to get rid of the attack matrix table.