Why would a polarized plug not fit into a polarized extension cord?
Since the question is &quot;why&quot; I'll try to answer that at the risk of many irate downvotes .. because one, or the other, or both, is not quite to spec!   I guess that's obvious.
This question reminds me of the vast difference in design and engineering between American and British plugs and sockets.   Two ends of the spectrum.  The British ones with their longer ground pin, little plastic doors on the sockets (live terminals blocked until ground pin inserted), individual switches, individual fuses, finger knurls, 90 degree exits (it's impossible to yank one out by pulling the cord), and physical strength that easily holds even the largest PSU snug to the wall.  There is more design and engineering in them than in some cars.   And the American ones .... your question says it all.   Crappy ill-fitting plugs dangling loosely from walls with people taking dremels to them just to get them to fit.
So much for &quot;why&quot;.    I've frequently filed down an oversized neutral spade on a power plug to get it to fit in a socket.  Use a hand file and be very very subtle.  As soon as it fits, stop.  Then try to insert it backwards ... if it fits, you've gone too far. Cut it off and install a better plug.