You presented this as if it's a valid form of logic
P --> Q
¬P
=====
¬Q
Now, I have countless sources online that call this a logical fallacy, Denying the antecedent. You, for some reason, don't want to look at any websites but just for thoroughness, I'll link a few.
https://web.stanford.edu/~jonahw/PWR1/LogicalFallacies.htm
https://www.britannica.com/topic/denial-of-the-antecedent
https://onlinelibrary.wiley.com/doi/abs/10.1002/9781119165811.ch3
https://philosophyalevel.com/posts/if-p-then-q-modus-ponens-modus-tollens/
https://www.oxfordreference.com/display/10.1093/oi/authority.20110803095711627?p=emailAMbd16BqHZ1a6&d=/10.1093/oi/authority.20110803095711627
https://philosophy.stackexchange.com/questions/59356/is-this-an-example-of-denying-the-antecedent
But you don't like online sources, so fine, I said I could disprove it with a simple example, so that's what I'm going to do:
All squares are rectangles - this should hopefully be an uncontroversial statement. Not all rectangles are squares - this should of course also be uncontroversial.
I have a bag full of paper shapes I've cut out. Some of them are squares. Some of them are non-square rectangular cutouts (like A4 pieces of paper). Some of them are triangles.
I pull out a piece of paper, and I tell you "I'm holding a square". Given that information (and this isn't a trick question, so you can assume I'm being truthful), can you conclude I'm holding a rectangle?
All squares are rectangles, so YES, you can conclude I'm holding a rectangle.
P is the statement "FJ is holding a square"
Q is the statement "FJ is holding a rectangle"
P --> Q
I hope all of the above is agreeable enough. FJ is holding a square implies FJ is holding a rectangle
I throw that piece of paper away, and I pull out another piece of paper. This time I tell you "I'm NOT holding a square."
¬P
Now, if your logic holds above, then
P --> Q
¬P
=====
¬Q
I'm not holding a square
====
I'm not holding a rectangle
But is that valid? Is it valid that, if you know I'm not holding a square, you also know that I'm not holding a rectangle?
If you don't think that's valid - if you understand that I could still be holding a rectangle, even when you know that I'm not holding a square - then you intuitively understand why denying the antecedent is a logical fallacy, and an invalid form of argument.