I remember that, what punkfolkrocker said, tapping cassette cases on the table. He can't hear me now, he's in the bathroom, but I remember I used to do that if the tape was stuck in one place and the tape drive motor wasn't strong enough to get it moving. After a few hard raps and a spin with the pencil it would play normally.

A tape deck with a stronger motor might have forced the tape to move, resulting in a squeaking sound, eh?

I remember, too, in line with what several people have said, that the tapping and spinning was usually only needed with pre-recorded tapes and with some cheap blank tapes that I bought before finding out how much mechanical trouble they caused. After that I only bought expensive blank tapes and LP's.