The list of reasons can be long. Bent/twisted links or teeth. Wobbled rings. Really bad chainline. Very work chain/teeth. Ft der that's very poorly aligned/cable tensioned/bent. Rider's leg/foot contacting chain during pedaling. Riding over really sharp bumps allowing chain to jump around. BB condition so loose that the rings move side to side. Same with loose ring/arm mounting bolts. There are more reasons but these are the first ones that come to my mind.

But, usually, the reasons is easy to figure out by carefully watching what actually is happening. If the chain will derail/fall off if you just rotate the cranks and not ride at the same time then watching the chain and ring meshing is pretty easy to do with the bike held off the ground (or up side down). Touching each part and seeing if there's any slop or looseness. Looking down the length of the chain as it slowly is pedaled around to see if any links are out of line. Spinning the cranks while looking down and between the rings for wobbles, bent teeth or the rings' spacing apart changing. Moving the ft der with only the cable while pedaling to see how the shifting works looking for the der cage catching on, moving too far/not far enough, broken der not moving consistently.

For an experienced eye this assessment usually takes only a few moments to note all the relationships involved. If the OP can't manage this process of discovery then perhaps a LBS needs to be asked for help. Andy.