I downloaded this icon from flaticon and want to reduce the thickness of the path:
I followed the guide here: http://projectwoman.com/2011/05/make-a-path-bigger-or-smaller-in-illustrator.html and used the offset path function but it just doesn't seem to do anything if I make the offset a negative number:
If I make it a positive number, I can see the paths will increase in thickness. Why will it not reduce in thickness if I make it negative?
You're having an issue, because the source file is tiny.
To illustrate this, I increased the object's size by 500% (Object > Transform > Scale):
At 500% scale, you can finally begin to notice the offset path (-1 px here):
I would increase your object's size, to begin with. Alternatively, you can try to mess around with small decimals to offset your path, but that seems much more difficult, to me.