Compared to 5.25" and 8" floppy disks, the 3.5" weren't very floppy. They didn't bend that easily, were stiff compared to the older formats.

Paragraph from Wikipedia:

Generally, the term floppy disk persisted, even though later style floppy disks have a rigid case around an internal floppy disk.

Where there people who refused to call 3.5" floppy disks floppy disks because they weren't floppy enough?

Over here in the boonies we used to call em diskettes.

They were floppy inside

People loved saying the word floppy and this correlated well with another 3.5" object that could reasonably reach 5.25" or even 8" when less "floppy."

Maybe... But "Hard Disk" was already taken. 🤷‍♂️

That's very close to german: Disketten.

Nope

I was still a kid in the '80s, but basically grew up around (and in, sometimes), computer stores and computers. I don't recall hearing this.

Danish disketter as well.

Aren't we all.

The housing was kinda rigid but the disk itself was real flimsy, says I who have used many floppy disks. Plus, in French we used to say 'disque' or even 'disquette' (a small disk) which did not relate at all to their floppiness, so to speak.

Disquettes in France.

My stepmom actually insisted on calling 3.5" floppies "hard drives," because of the casing.

I'm not sure she ever got over that mistaken assumption before they eventually faded from use, lol.

They were also square. We still called them "discs".

in portuguese we called them disquete

Yes.

The disc inside is still round though. Did you never crack one open to see?

In their dreams

Of course I did. OP is asking if our description matched the inside or the outside, I'm giving further evidence that the (rigid, square) casing didn't affect that description.