I think there's basically a progression flying combat.

At first, you don't have any depth perception, and you spend a lot of time flying around behind or in front of everyone else (usually behind though). At this stage, there aren't many cuts, but there aren't many mid-airs either. Some guys skip this or go past it quickly because they have good natural depth perception and are used to placing their model where they want it.

After that, your depth perception gets better, and you can "see" one other plane besides your own. At this point, you start getting cuts, but you really start getting a TON of mid-airs, especially in SSC. The mid-airs are there because you can get your plane to the same depth as the other guys, so you spend a lot more time a lot closer to the other models in the air. And in SSC, the planes are slow and turn tightly, so they stay in the same area most of the time, and that means a lot of mid-airs.

After you've been flying for a bit, you start to recognize what the other guys are doing in the air, and you can watch multiple planes at a time, watch traffic and see where they are going. You can predict where a plane will be, and most importantly, you start flying "around" the other planes, making moves to avoid mid-airs and set up at the same time. The key thing is that you can see where another plane is going, and you can see bad angles like head-on approaches coming, and get out of the way.

Some guys pretty much skip the first, and some guys never quite manage to get to the point where they can see the whole sky and follow and avoid multiple planes at once.

Personally, when I want to cut someone in SSC, I don't fly towards them, instead I fly around them, so that I come around behind them. Flying directly towards a plane you want to cut is a great way to get a head-on mid-air, but not a great way to score cuts.

Also note that there are two different styles of flying combat. Some guys "furball" while other guys fly persuit. Personally, I'm mostly a persuit pilot, so I pick a target and chase them until I get a cut. Furball pilots will generally hang out in one part of the sky and wait for someone to get near them (usually circleing in the middle), then make a quick adjustment for a cut.

And finally, I notice that you said you're trying to intercept streamers, I assume that means cutting through them at a sharp angle. It usually is easier to get behind someone then turn with them and go through the streamer when they turn.