If the AI is flying past you on a straight, what happened is that you took the last corner too slow and had a lower exit speed than the AI, which allowed them to catch up and overtake you. It's not drafting, that has an effect but it won't lead to the AI flying by you, only catching up. The rubberbanding in Driveclub always works in your favor--the AI knows the perfect racing line, but will deviate from it to keep the pack around you.
I can understand your frustration, you probably expect Driveclub to be more arcadey than it is. I did too, but I realized that it's actually grounded in serious racing fundamentals. The cool thing is, getting good at Driveclub teaches you to be a better racer.
The most important factor in getting a good time is to maintain high corner exit speed. Think about it this way: any speed you lose from braking too late is gone for the rest of the race. You can never make it up. That means you have to brake early enough to hit the apex to maximize the amount of time you are accelerating between corners. If you brake too late, two things happen: 1) you miss the apex or hit it unsmoothly 2) you slow down too much because you have to make a tighter turn because you missed the apex. This kills your corner exit speed, which means you have to spend time getting back up to speed, which lets the AI get past you.
It's frustrating at first, but if you stick with it and learn from your mistakes, you will see yourself improve. There is no better feeling than being 10 or 15 seconds off a challenge time, and thinking it's impossible to get, and then getting it an hour (or day) later because you've improved as a racer.
Also, there's a pretty big difficulty spike when you get to performance class. Those cars get very slippery at high speed, and it's easy to lose control and spin out. You'll learn how to make tiny, tiny adjustments.
I honestly feel like Driveclub's structure is great for picking up and playing. It's fairly easy to get enough stars to unlock a lot of tour events, and then you can pick and choose from them to find races you feel like playing. Since most events are under 5 minutes, it's easy to pick up. Yes, you will have to retry things a lot, but if you restart races as soon as you make a major fuckup, you won't "lose" too much time. I can easily lose an hour retrying a single event, and it'll be a great hour.