When a person passes away, the magnetic field of the spirit does not fade. It is said to be in the subtle body. (We are all in a magnetic field and you and I are affected by it.) So as long as they are in that subtle body we pray to them, and they come and partake of that food we offer at the sraddha or funeral ceremony.
If you do this for your father it is good. You may eat that food because your karmas are alike. If you do it for your mother it is good because once again your karmas are alike. But we don’t want to mix up our impressions or karmas with anyone else, because that makes it difficult for a sadhaka [spiritual aspirant] to concentrate.
Another reason for not eating the food at a sraddha ceremony is that often they offer fish, wine, brandy etc. [laughter] As it is prasad [sacrmental food], how can you leave the wine and only eat the other things?
A sadhaka who wants to go towards God should pray for the souls of the deceased to get liberated, rather than calling the souls again and again by giving them food and making them some sort of devata [demi-god].
If your father was alive would he eat and leave me half his food to eat? No. So, after he has died - and after you have offered it to him at the sraddha - why would you offer his leavings to me then? This would be worse still. You are embarrassing him wherever he is.
But if you eat the food as his daughter or his son then it is good. He will be happy. You can safely take your father’s food, your husband’s food or your child’s food and eat it.