What does しょうがない Shouganai mean?

Shouganai says that there is no way of doing something. It is a contraction of a longer phrase built from 仕方 (shikata), a way or a method, and the negative: no method exists.

What the phrase actually claims

Something narrower than resignation. It is a statement about the availability of options, not about willingness to pursue them, and its practical function is to close a topic: the situation has been assessed, nothing can be done, further discussion is not useful.

Delivery does the rest. It can land as weary, as brisk, or as fond, and an adult saying it about a child's behaviour is not despairing about anything.

The fatalism reading

English commentary reaches for this phrase to argue that Japanese society is passive in the face of misfortune, tolerant of what should not be tolerated, or disinclined to complain. The phrase gets cited as a window into national character.

The comparison that ought to accompany that claim is never made. English says it is what it is, nothing to be done, no use crying over spilt milk, and that's life, and nobody adduces those as evidence that English speakers are fatalists. They are read, correctly, as ways of ending an unproductive conversation.

Why the double standard is easy to fall into

A foreign phrase arrives without its ordinariness. English speakers meet this one in subtitles, at emotionally significant moments, chosen by writers for scenes where something has been lost, because those are the moments that get written about.

The everyday uses, about weather, trains and minor inconvenience, do not appear in the sample. What survives is the dramatic subset, and a dramatic subset of any phrase looks like a worldview.

The fair version of the cultural claim

There is a real question about when a society treats a problem as structural and therefore fixable, versus given and therefore to be absorbed, and that line does differ between places and over time. That is a claim about institutions, and it is arguable with evidence.

It is not a claim about a phrase. The phrase is a conversational full stop, and English has a shelf of them.