It tends to stop once you get behind someone (top tip - Good Dogfighters make the best dogfighters... Consider Eagle, Viper, Vulture - according to budget). "Jousting" mainly happens when you allow yourself to overshoot the target and must turn back towards it. They're doing the same - of course - so by the time you've both come about you're kilometers apart and keen to reengage, so boost back towards each other. Basically it's just a "top trumps" battle of the shields. The trick in avoiding it is to start to turn *before* they pass you, so that by the time they pass you you're gone past 90 degrees, and are almost facing back the way you came, with their thrusters pointed at you. Then shoot them. Never be too keen to close on a dangerous target - you're presenting your canopy to them to be shot at, they will get as much shooting time as your do before you pass and you may collide (usually disadvantaging both ships..).
Practice dogfighting - there is more to it than simply trying to get your crosshairs on the enemy and pulling the trigger. You must consider where your and their advantages lie (who has best shields, who is faster, who has bigger guns!) and play to/against those advantages. You must also learn to predict what they are likely to do and avoid situations where you will not have an advantage. As has been said, F/A off will allow you to turn more quickly (as will keeping the throttle in the blue sector), but will also cause your ship to "slip" like crazy, which is a useful way to dodge sometimes, but can mean you're travelling in a straight line whilst rotating, which makes you an easy target and doesn't close on the enemy.
If you want to practice with little risk, either go and buy an eagle and be prepared to lose it a few times (top tip - be realistic. anything above a cobra is unlikely to be a viable target), play Arena (a GREAT way to practice combat - and you will earn rewards doing it) or simply use the training missions (zero risks!)