Confused about AD&D 2nd Edition Non-Weapon Proficiencies?

You're reading it wrong, yes.

That's a modifier to your base score, which you want to roll under. So...-2 is not a benefit, but a penalty, while +1 is a good thing.

The modifiers are to your score, not your roll.

In 1st Edition, it was simply, make a dex check to jump from your horse onto the guard to tackle him to the ground. If you had a Dex of 15, you would have to roll 15 or LOWER

In 2nd Edition, you had to have a proficiency to do certain tasks. Other tasks required a stat check. For the riding jump and tackle example, you need the riding proficiency. Let's say you are doing this from the back of a pegasus and you have an airborne riding proficiency. This means that you must roll lower than a 15 on a d20. However, you must add modifiers.

Let's say you have 2 slots in airborne riding = +1

The proficiency gives you an innate modifier = -2

Your pegasus is wearing a special saddle = +1

Your target is a size above you = -4 (just an example)

add those together and you get -4 as you total modifier. You combine that with the 15 that you have for you initial base check and you get an 11. You must roll LOWER than an 11 on a d20. As you see, modifiers that subtract do not benefit you because you are subtracting from the score you must beat, not the roll.

This is the main difference between 2nd edition and 3rd edition. In 2nd edition, you combine modifiers into the score you are trying to beat with the roll. The number from the roll is always pure and unmodified. It is only compared to a score that you must roll over or under. In 3rd edition you can get modifiers to your roll or the Difficulty Class Score/Armor class. The two are in contrast to each other.

By sticking to ONE weapon, you will level up that weapon. The higher level the weapon is, the more proficiencies it get's. E.g Kick, Red Dot, Acog, Camo e.t.c To get that achievement, you have to get all the proficiencies on a single gun. Hop this helped