Why don't we use the indefinite article with 'software'?

Generally, one doesn't use the indefinite article with a noun because it's plural, but sometimes you get nouns where, for some reason, the indefinite article isn't used even though the noun is singular. I would never say 'a software', though it seems to be a singular noun, and I've heard it said (though it sounds wrong). Instead, we say 'some software' or 'a piece of software' (the latter implying that software is singular), so why does 'a software' sound wrong?

EDIT: I really meant to ask why we don't consider software singular. Maybe I should have asked, 'why is software a mass noun?'

That's because software is uncountable, or a mass noun.

In English, mass nouns are characterized by the fact that they cannot be directly modified by a numeral without specifying a unit of measurement, and that they cannot combine with an indefinite article (a or an).

Edit: in reply to your edit, the key here is -ware:

1. Used to form nouns denoting, collectively, items made from a particular substance. glassware
2. Used to form nouns denoting, collectively, items of a particular kind or for a particular use. giftware

Note the word "collectively". Software was coined in 1953 by contrast with hardware. You wouldn't say "I need two new hardwares", either.

I remember being told once that software was originally jargon in the Victorian refuse-collection industry, where it meant "things that would decay or decompose", as opposed to hardware, which would not.

If this is so, and I can find no source for this on the internet, it would seem to be a non-count noun, as in that trade one would not count individual apple-cores, dead rats, and so forth, but be rather concerned with the bulk or weight ("I've picked up ten hundredweight of software").