It is possible you are right and it was just a coincidence - but it is also possible that the vaccine was the trigger for ALS to develop. We don’t have enough evidence yet to confidently say
You linked to a single case report. It does not establish any type of causal link at all. That single person was most likely going to develop ALS at the time whether he had been vaccinated or not.
What data do we have on the incidence of ALS between 2019 and now?
Even pre-2019, there appears to be a slight increase in incidence of ALS over time, although not statistically significant [0] – which could mean the increase isn't real, but could also mean it is real but studies thus far have lacked the statistical power to confirm it.
So, if it is true that ALS incidence is increasing anyway, the question then must be–has the rate of increase accelerated since 2019? I'm not aware of any published data on that topic. Furthermore, there is also some evidence that COVID-19 infection can be a trigger for onset of ALS in susceptible individuals, [1] so even if there is some pandemic-associated acceleration in incidence increase, it may be difficult to disentangle to what extent it is due to infection versus vaccination.
> You linked to a single case report. It does not establish any type of causal link at all.
A case report – even a single one – is evidence. Only weak evidence, but even weak evidence is evidence. Certainly not strong enough to establish anything - but a single case report is enough to increase the epistemic probability, even if only by a little bit. Establish is more systematic review of multiple high quality studies territory, which is at the opposite end of the strength of evidence spectrum from case reports.
I think we are likely talking about something with a rather small effect size. With a sufficiently small effect size, something can be entirely real but also impossible in practice to statistically demonstrate.
You seem to be comfortable letting the parent state the vaccine was the cause, but uncomfortable with anyone challenging them on that. If “neither of us know”, why are comfortable with the former but not the latter?