We’re pretty sure Kate doesn’t actually think Randall is an illegitimate Pearson or incapable of carrying on Jack’s legacy, and if Randall really sat and thought about it, he’d probably realize his sister more than likely misspoke.
Randall does have a track record of making incredibly uncomfortable family moments with confrontations, so it’s unsurprising he’s wasting no time in calling out Kate for the statement.
Unfortunately, the adopted Pearson is in a weird place right now and in a mindset where he’s feeling like an outsider wherever he goes, so we doubt his cooler head will prevail before starting a classic This Is Us sibling throwdown.