In todays generation when there is leftover bread or Challah we often discard it. As bread is the food for life there are those that either feed it to the birds, make kugel, breadcrumbs, etc. instead of discarding it. Is there an Issur of throwing bread away?
Destruction of any object or food that is still usable falls under the catagory of Lo Sashchis (Rambam Melachim 6:10)
I sometimes leave the bread out until it stales and is no longer edible to the norm of society. Alternatively, I throw it in the garbage inside a bag so that the bread is preserved in its state.
I don't know from where I remember this:
The bread part that is less then כזית could be thrown away.
from below i see that it is forbidden to destroy a kezais (olive size) of bread
and it is permitted to destroy bread less then a kizais but in a respectful way
talmud brochois 52b
... the crumbs which are as large as an olive and leaves those which are smaller than an olive. This supports the dictum of R. Johanan; for R. Johanan said: It is permissible to destroy wilfully crumbs [of bread] smaller than an olive. *7 ...
*7 In spite of the prohibition against wasting food.
... may be wantonly destroyed, the deduction being from the statement, BECAUSE THEY ARE FOOD FOR ANIMALS, which may be destroyed.
...[This practice should be followed] lest pieces [of bread] the size of an olive be found on the floor. It is forbidden to walk or wash over [pieces of this size]. If, however, the pieces are smaller than an olive, it is permissible to destroy them intentionally.
shulcha aruch harav orach chaim 180.5
אע"פ שמותר לאבד פירורים שאין בהם כזית בידים לא יזרקם במקום דריסת רגלי בני אדם מפני שקשה לעניות כשדורסים על פירורי לחם ולא התירו אלא לאבדם כגון להשליכם למים וכיוצא בזה
even though it is permitted to destroy crumbs that do not have a kezais (size of an olive) with your hands, do not through them in a place that people walk, since it is bad (eufemizm) for poverty then they are stumped on, they did not permit it only (they only permitted) for example to through them into water and similar things
may be it is permitted to cut the bread into peaces less then a kezais and the to destroy them, and maybe it is forbidden since by cutting it you are destroying it (making is useless)
If it is good it should not be thrown away.
However, I have seen that some people dump such bread in public places, allegedly to feed birds, causing a mess and possibly unhealthy conditions. They should only do that on their own property or in a place where they have permission to do so.