At first, you just think Poe is being snarky and posturing because “HE’S THE COOLEST PILOT IN THE GALAXY AND IT’S HOLLYWOOD MOVIE RULES! YOU CAN’T BACK DOWN FROM THE VILLAIN!”
You watch their scenes again, though: Poe is clearly bemused by Kylo and what he’s become. He’s seen behind that mask.
He’s still scared, obviously. But he seems to know, for a fact, he’s not quite dealing with a monster here. Because he knew him before.
When Obi Wan takes Luke to Mos Eisley, what if he’s actually looking for a specific pilot? After all, it’s a wretched hive of scum and villainy, Obi Wan would be smart to find a pilot he could trust. Who else would he turn to but someone sympathetic to the Jedi, who fought alongside the Republic during the Clone Wars and whom Yoda considered a great friend?
He was specifically looking for Chewbacca. Han just happened to be the obnoxious dead weight.