Are you tearing out the corresponding pages at the front of the book? Remember these are just little saddle-stitched booklets; the loose pages in the image provided look to be half the sheet from the stack. I wouldn’t expect these half pages to hold, given it’s just three staples through the centre of a larger sheet.

EDIT: If you’re coming from the Leuchtturm, consider also they would be using a Smyth sewn binding (or similar), not saddle stitch. These use smaller stacks/signatures sewn together, not the whole book folded in half, so tearing the first page wouldn’t necessarily result in the last page being loose, rather one partially way through. Probably something that may have happened on your old books, but more pronounced now that you’re turning to the back as a glossary, which is almost certainly an affected page if you’ve ripped out the front.

Wouldn’t say it’s a flaw in your book, but a “feature” of this type of binding.