A Split-S and an Immelman, two of the most basic air combat manuevers invented in the days of wing-warping monoplanes using 80HP LeRhone engines, can be done in any air combat game. That ranges from way back when in the most basic of air combat games: 1942: BattleHawks to the most modern of air combat games that push the envelope towards "simulation".
A split-S is going forward at anywhere from 140MPH to 300MPH, rolling inverted and easing back on the stick until you are pointed opposite the direction you were traveling but a couple hundred feet lower than you were before.
An Immelman is flying forward at anywhere from 250MPH to as fast as you can go, pulling back on the stick into a half loop so that you are now traveling the opposite direction you were before but a couple hundred feet higher. You must now roll your plane right side up.
Both of these simple manuevers can be completed in Aces High. You are either pulling the aircraft into a stall because you are pulling too hard on the stick (believe it or not, this is the way real aircraft work) or you are too low on speed to complete the Immelman.
As for the Split-S, if you can not complete one of those without stalling out or gaining any speed, then yes you are doing something wrong.
As for the car analogy, I'd like to see you jump from driving an automatic all your life into a stick without any experience.
I guarantee you it will take more than 5 minutes for you to get accustomed to the gear thresholds and the sensitivity of the clutch.
Don't expect to be able to yank your joystick to the maximum of the pitch axis without stalling out the planes. That might work in simpler games, such as Fighter Ace, Screamin Demons Over Europe, European Air War, or any of the other simpler boxed air combat games, but it doesn't work with games that are focused on the accuracy of the portrayal of flight- such as WarBirds, Aces High, or Il-2.
The rest of the games out there are child's play.
-SW