do the sororities make first picks?

If you pick your top 12 for philanthropy and all of those houses pick you on their lists, you go back to those 12 houses. However, if one ( or more) of those houses release you from their list but another ( or several) house(s) have you on their keep list, they get put on your schedule. In some instances, a house you might “rank” over several rounds keeps showing on your list. Some girls are mad about that and say rude things like “I can’t seem to drop them, no matter what I do”. However, that house saw something special in you, something that other houses didn’t, and want you to be part of their sisterhood.

It’s very rare a pnm gets all their picks.

Even “full cards” are hard - meaning just getting the max houses each round is good, even if they aren’t the ones you rated your favorites.

Most PNMS do not even get full cards. .

PNM's do not drop houses, only rank them in order of preference. The sororities do the dropping. When any of the houses you want back release you, (when not if) the algorithm automatically adds other houses back for you, based as closely as possible to your rankings, to make sure you have as full a schedule as possible.

The better pnms drop the worst houses.

The better houses drop the worst pnms.

Plain hard truth.