What it means
Sealioning is when someone derails a conversation by relentlessly demanding evidence and politely badgering you with question after question, all while pretending to be perfectly reasonable. The fake politeness is the weapon, you can't lose your temper without looking like the rude one, even though they're wearing you down on purpose. It's harassment disguised as just asking questions.
Usage examples
"Every thread he joins turns into sealioning, fifty polite questions until everyone gives up."
"It's not real debate, it's sealioning, he just wants to exhaust you into silence."
"He wasn't debating, he was sealioning her for an hour till she muted the chat."
"That bloke does the whole polite little question dance, but it's just sealioning with a clean shirt on."
Where it comes from
It comes from Wondermark, a 2014 webcomic by David Malki. In the strip, a sea lion keeps politely following a couple and demanding evidence for an offhand comment, long after any normal person would've let it go. People online grabbed that image fast, and sealioning became the name for this bad-faith routine.