Why do I have to show my ticket stub when entering an airplane?

Here's the situation: I have just had my ticket scanned at the gate and happily walk through the long gateway toward the plane, giddy to get on board, because I even after all these years I love flying. I happen onto the queue of passengers waiting to enter the plane, so to keep myself busy, I put away my precious ticket stub (I'll need that for the expense report) into one of my pockets.

Finally, it's my turn to enter the plane, and the flight attendant asks me where I sit, and I reply it's 41k, which is over there (I've taken this exact flight many times this year already).

Then he asks me to see my ticket stub, so I have to go through all of my pockets because I already forgot where I put that stupid thing, which makes me that guy who prevents everybody from getting on board. Awkward.

Why do they want to see my ticket stub? I just showed it at the gate, together with my passport, so I'm totally on this flight. And while I may be bad at remembering pockets, I'm good at remembering my seat number correctly.