I've noticed that some pilots turn off the climate control for start up and takeoff, like the Sr22. Why is this? And has this been phased out with new technology?
Assuming there's a heat pump system involved (as with home and auto air conditioning), it draws considerable power from the engine, and is also subject to unpredicted pump seizure which can result in sudden power reduction (when it's needed most), start a fire under the cowl, or even completely stall the engine (I've had a seized pump in a car cause the engine to stall, requiring me to cut a drive belt to continue driving -- not something you can do at 13,000 AGL or fifteen seconds after rotation during a takeoff).
Turning off the climate control compressor during takeoff seems a minor precaution to prevent this possibility, and it wouldn't surprise me at all to learn that aircraft that depend on a heat pump for cabin climate control would recommend disabling that item during critical periods.
Some newer automobiles have electric motors driving accessories that used to run off the engine via drive belts (my current car has electric power steering, for instance, and electric cars, of course, have electrically powered air conditioning). Using electric drive for a heat pump might still require shutting that heavy power draw off during startup (the battery can only supply so many amps), but would eliminate the need to keep it off during takeoff and climb out.
More or less addressed in my answer to this similar question but aircraft POH data is typically derived from full power numbers which means the engine is driving power only to the propeller and the alternator for required electrical systems for the given flight regime. Since engine power directly impacts aircraft takeoff performance you would not want something arbitrarily reducing that power at a critical time or causing another potential failure point.
Its worth noting that this is not a technical limitation its a "safety first" way of operating aircraft, certifying them, and generally thinking about flying. You can technically run climate control during takeoff nothing is physically preventing it other than your takeoff performance numbers.
I can't say for sure with airplanes. But with a typical internal combustion engine car, when you start it up the air conditioning (and some other accessories, depending on the car) turn off when you move the ignition to start, and after the car starts and you move back to the run position, the air conditioning starts running.
Why? Air conditioning is a huge power drain. In fact, a car air conditioner can produce as much cold air - and use as much power - as an air conditioner for a small house (2 to 3 tons). I suspect airplanes are not much different.
In addition, in a car the concern is simply "power to start the engine". In an airplane it is "power to start the engine and to get safely off the ground". Takeoff requires more power than cruising and, as I understand it, takeoff and landing are the most dangerous parts of a typical flight, so making sure the engines have all the power they need for takeoff is critical.
Engines on some larger aircraft are started using bleed air drawn from the auxiliary power unit. This same bleed air is used for the air conditioning while on the ground without any engines running. Therefore in order to ensure a successful engine start, the air conditioning is switched off so that all the bleed air from the APU is available.