Why are spiders afraid of flies caught in their web?
from https://www.researchgate.net/figure/234696071_fig5_Figure-1-Differences-in-attack-strategies-upon-safe-and-dangerous-prey-in-orb-web



The linked article is pretty cool.  Bottom line: predators need to be careful.  If they get hurt they cant hunt and they starve.  Spiders have different strategies depending on perceived dangerousness of a prey item.  The linked article, for example, categorizes dipterans (flies) as nondangerous to spiders but orthopterans (crickets) as dangerous.  How are crickets dangerous?

For your spider I can think of 1 of 3 things.

1: Fly is dangerous to spider in a way not obvious to you.  Maybe it is poisonous, or can bite, or has sharp spines on the leg.

2:  Fly is perceived by spider as similar to dangerous prey.  I have watched spiders address wasps in their webs and the spiders are careful.   If there are flies that mimic the appearance of wasps / bees to get respect, why not one that behaves in the web like a wasp to get respect?  A cool idea and testable too.

3:  What you see is the danger.  A big fly thrashing around might be enough to damage the spider.  A spider not desperate for food might not want to risk getting hit.  Spiders are not that durable.  That makes sense to me.