Why do some cars lose acceleration when the A.C is on?

Like in my 2007 Versa Sedan SL, I have to turn the AC off when merging on the highway otherwise it feels like driving a Ford Model T.

But my 2010 Odyssey, and 2017 Rogue can drive perfectly with the AC on. Heck on the Rogue I can drive on ECO and still merge fine on the highway.

Yes, the AC compressor takes a lot of power to turn. If you had a 500 hp car, you wouldn't even feel the compressor cycle on-and-off. I'm not familiar with the Versa, but assume it is horsepower-challenged.

Two cars I had long ago - a Chevette and a 4 cyl Mustang - were so underpowered that there was a device to automatically turn-off the compressor when idling, acceleration… Even when going-up a hill.

The air conditioner in your car takes power from the engine to drive a compressor that creates the cooling effect. SOME cars (But not all) have a built in sensor that automatically disables the air conditioner compressor when more power is needed from the engine for acceleration.

The A/C compressor is engine driven on most vehicles and when it is engaged, it does become a parasitic draw on the engine's power output. If the engine is on the smaller side, this becomes more noticeable.

Many vehicles will recognize if the driver is accelerating hard and will temporarily shut off the A/C compressor during this time.

Depends on the size motor you have.

I was told by one car dealer that A/C uses upto 20bhp, so it depends on how many you have to start with.