I've beaten a 1970 before. Is there that much of a difference that no matter what I do the only way that I'll beat a 2000 is by pure luck or not at all?
How do I beat a 2000+?

This isn't something that I say very often but kaynight is (somewhat) correct. I have no idea why you are looking for a psychological reason for having never beaten somebody 500 elo points higher than yourself.
Maybe a better question is, how has somebody who is still at school and who has no special talent for the game played enough chess in their lifetime to have beaten several players against whom they should score ~9%? That just doesn't seem plausable.

Okay, I may have exagerrated slightly when I said several. If my memory serves me correctly, I've beaten at least 4. Does that change the situation at all?

Also, the reason that my rating is 1500-1600 is because I tend to be inconsistent. I've had really bad tournaments which have set me back on quite a few occassions.

Also, the reason that my rating is 1500-1600 is because I tend to be inconsistent. I've had really bad tournaments which have set me back on quite a few occassions.
That's pretty much it: the difference between 2000 and 1600 levels is often not in the chess knowledge - both levels are quite advanced - but in consistency: if you beat 1900 player, but then lose to 1400 because of a momentary loss of concentration, you'll be in 1600 for a while. Once you become more consistent, your rating will go up accordingly.

Okay, I may have exagerrated slightly when I said several. If my memory serves me correctly, I've beaten at least 4. Does that change the situation at all?
I don't consider that an exaggeration. I do consider it implausable. If your entire 9% came from wins (no draws) then you should have played approximately 44 players in the 19-2k bracket to have beaten 4.
Now of course on top of that we have to consider that you are young, so not only have you not played that much chess but you have certainly not been at your current rating for very long, before which time your chances of beating such players dramatically descreases even further. I will be generous and say that 10% of your current opponents are in this rating bracket. That means that you have not improved in your last 400 tournament games.
I can go on and on, like about that 9% actually includes a huge percentage of draws and you are more likely to beat this level of player ~4% of the time (100 required games).
Are you beginning to see why I am struggling to believe what you are saying?

I do understand your disbelief in what I am saying, and I will be the first to admit that my wins are very statistically unlikely.
I know that the number of 1900's that I've played is nowhere close to 100. It's probably somewhere close to twenty. So, out of those 20, I've won 4, drawn 1, and lost 15. That seems like a good estimate, although I can probably go check my games to see if that's accurate.
I can tell you that out of the three 1900+ players that I know the results of off the top of my head.
Player 1: 2 losses, 1 win, 1 draw
Player 2: 1 win, 1 loss
Player 3: 1 win
There are most likely others, but those are the ones that I specifically remember playing. However, I have played 9 games against 2000+ rated players, all of them being losses. Take that as you will.

the further you go up 'the ladder' of ratings the more technical you have to be, like exploiting small strategic weaknesses in positions, rather than looking to win material straight up. guess its more about your technique when your playing

I believe you. I had a point and it wasn't just to call you out. My point was that you shouldn't be using statistically unlikely likely results as evidence that you possibly have problems against 2k+ players. In fact, those 29 estimated results that you have stated (against all of your 1900+ opponents) score you better than you should against an 1850 opponent.
Don't worry about not having beaten any 2k+ players. Just like your performances against the 19-2k players, your games simply aren't statistically significant. More than likely, you don't have any problem at all against 2k+ players.
I have no reason to doubt the OP. Some of the replies sound like jealousy to me, but what do I know.
To beat a much higher-rated player (+200 points), in general one must try to get an advantageous situation in which the higher-rated's knowledge/skill advantage is not helpful to them.
For beating players 2000+ there are a few considerations:
1. If the 2000+ plays a less-than-mainline opening, you need to act decisively and not let them get away with it. "Not letting them get away with it" means gaining a development lead, or a central space advantage, or good attacking position on one of the wings.
2. It is imperative to play incisive moves that get to the point strategically. No dilly-dallying with time-wasting excessively-prophylactic moves.
3. Believe in your ideas, don't doubt yourself, and don't allow your opponent bluff you.
4. If they offer you a draw, it means your position is anywhere from large advantage to decisive advantage.
Good luck!

Thanks, Andre_Harding. That's actually a big help. Most of my games against higher rated opponents seem to work the best for me when I attack, despite my attacking skills being fairly weak, in my opinion. I'll try and be more aggressive next time I play a 2000+ (given that the position allows it of course). If it fails, that's just fine because that's the expected result anyways. Thank you.
@chessdude46:
The best way to beat a higher-rated is a direct attack. Even 2600 GMs collapse sometimes as a result.
The problem is that it's hard to not get too carried away and go all-in prematurely.
Trying to beat a much higher-rated by defense (take material and hold it) virtually never works.
When I'm playing at my best, I've tended to play somewhere around a 1600-1800 level. I've beat several 1900's, including one that was such an upset it got published. However, whenever I play someone who's anywhere above 2000, I always seem to collapse. I've played really good games against them, and I've even been in situations where 30 or 40 moves in the game is even. I always seem to make one mistake or miscalculation that makes me collapse. Is there any sort of chess advice that would benefit me here, or is it entirely psychological?