Part 12: "You Musta Pissed The Gods Off" by Sleep of Bronze.Spite is one goddess, not all of them.
Genuinely, lots of the handed down summaries of myths that you might read in your native language don't have the depth of the originals, and typically there are more (and less) reasonable justifications for lots of the punishments.
Nevertheless, there are two additional reasons that a single fault might spell trouble for people around the dude who first fucked up instead of just him or her.
1) Religion is way way way more communal and political than in most modern day religions and societies. Particularly the western world after Protestantism and its impact on the way Christianity worked (both in the sense of the subsequent Protestant sects and the reaction Catholicism had to those sects.) You will especially notice that festivals and holy days involve city wide processions and ceremonies and sacrifices. The sacrifices themselves strengthen the communal air - if the city devotes a hecatomb to the gods, one priest is not going to eat the meat of a hundred oxen. That food gets shared out among everyone there.
Resultantly, if someone disrespects the immortals, fails to heed them, and is generally a shitty person, that's not simply their fault and it's not simply between them and their gods. It's everyone's problem because they should have been making them a more devout worshipper, should have corrected them if they could and so on.
This attitude is reflective of the anthropological theories of shame and guilt. Lots of modern day societies (and again, in the West, this was at least partly spurred on by the Protestant theology of the Reformation) would typically be described as guilt based. The 'moral' force which is meant to keep you in check is internal: you understand that you'll feel bad if you kick that beggar, and you do feel bad when you kick 'em. Greek society was more toward the shame end of the spectrum, where the moral force is external. You don't do a particular thing because people will find out about it and hate you for it; the gods will find out and hate you for it and maybe burn down your house. You are raised with the fear of disapproval more than with the expectation of nagging internal voice. Obviously, an external moral force falls down if you don't think you'll get caught or don't care about the consequences; an internal one is by nature less categorisable, and its failure points will be more individual. Most modern societies impose a kind of external force through law, and just sort of hope you get instilled with an internal one along the way, perhaps encouraging it or specific parts of it during education.
2) Death, and particularly the violent death of crime, was thought to generate a kind of metaphysical pollution, or miasma, around victim and perpetrator. Or the perpetrator is just polluted because they turned the living person into a dead one, either way. This is not a discriminate pollution: it sticks, so to speak, to people and places which come in contact with the dead, whether or not they had any initial involvement at all. (This probably results from both a certain understanding of disease and a societal imperative to discourage harbouring murderers.) You can suffer in this way even if you aren't the initially guilty person, because you actually fucked up by not identifying and getting the hell rid of the polluted criminal in your midst.
With a very few exceptions, mostly exalted founder heroes, this results Greek cities always setting aside burial grounds a good distance from the metropolis itself, to avoid the concommitant contamination.
If anyone read Tamora Pierce in their youth, she did some neat stuff with this in a pseudo-Greek city state in the book Shatterglass, where a criminal uses the fanatic devotion of the populace to cleansing the pollution of death in order to foil foreign investigators who want to have a detailed study of the crime scenes.