Analemmas are not really caused. They are just a record of speed changes. The sun accelerates decelerates during it’s 1 year cycle and if you take a picture from a fixed location exactly every 24:00:00 hours then accelerations and decelerations show as a deviance in what would otherwise be a straight line north and south. The north and south variance is due to the north south movement of the sun over the year. All objects have analemmas.
I’m assuming you are understanding it from a FE perspective. The reason why the analemma makes this shape with a bigger lobe on the southern side is because the sun has to speed up to maintain position when it’s circling outwards towards December 21st. What it is doing is accelerating but it actually over compensates or over accelerates which is why it arrives early for those period of days. It has a longer acceleration period when going south and has a longer deceleration period when heading back north. It would be like if you were driving on a highway that had speed signs every 10 miles going from 50mph to 70mph so you would accelerate to get to 70 but you would over compensate and hit 71 or 72 and when you saw the 50mph sign your would let off the gas but too much so you would hit 48 or 49mph. There are only 4 days in the year that the sun makes a rotation that is exactly 24:00:00 and that is where it is in the center of the analemma axis. It’s around the days June 12, August 31, December 24, April 14th.