Why does it matter whether or not the clutch is engaged slowly or quickly? How does this cause the engine to stall?
If you let the clutch out slowly, then as the clutch engages, it slips some and starts moving the car a little without stopping the engine. Doing it too fast would require the engine to provide more energy in a shorter time than it can do so it would stall.
This is a practice thing and may take some time. I suggest you have an experienced standard shift driver help you out a few times.
Note: it seems to be less of a problem with most modern cars, but it is possible to damage the clutch practicing this. An experienced coach and help reduce the practice time.
While my father was great, generally family members may not be the best coach.
Next step is to learn how to do it on a up grade.