It is never fun to have a fly buzzing around. Even worse when you are sitting down to a meal. Bad enough at a picnic, even worse in the house. Bad enough during the week, but on Shabbos... What makes things worse on Shabbos? Two issues -- trapping and muktzeh. We are not even going to talk about killing it, that would be forbidden even on Yom Tov since flies are annoying and disgusting, but not dangerous. Lets take the issues one at a time. Flies are muktzeh on Shabbos just like all animals. Pets can be taken for walks because of the prohibition to cause needless suffering to an animal. Flies; sure, just try getting a leash on one of those puppies. This, obviously, is a rabbinic injunction. What about trapping? Flies are certainly not a species that trapped for its skin (ewww), nor does it produce anything of particular value (such as venom); therefore trapping them is also forbidden by rabbinic -- and not Torah -- injunction. Forbidden is forbidden, of course; and as R' Fuerst is ...
This is a paraphrase of the pasuk in t'hillim 84:7 -- "mei'chayil el chayil" -- which means "from strength to strength". In this case, it is my thoughts and ideas to those who are strong enough to be interested :)