Okay, the long and sordid history of two spaces, now one.
A long, long time ago in a place far, far away, they invented typewriters. Pretty much all typewriters before the electric ones had the exact same amount of space per letter. In other words, after you pressed the key, the arm swung up and struck the paper, then the machine advanced the carriage by a set amount. This means that every letter had exactly the same width, even though a capital W took up far more of this space than, say, a period. Because a period floated out away from the letter, especially if the letter in question was also a thin letter like a lower case l, then two spaces were necessary after the period so that one could identify the line break.
Since electrification of type, nearly all type is proportional spaced. Notice there are no big gaps in illicit, nor does the type run together in AVAIL? Notice how the period is tucked in to its sentence and completely related to it?
So the first reason for only a single space after a period is: because it's not needed. The type is designed for only a single space.
There is an argument I hear a lot (especially at home), that a single or double-space is optional. Let me give you the second reason. Readability. If you use two spaces at the end of a sentence, it creates a gap. A gap that is greater than the gaps between words on the same line. This draws the eyes to it naturally, and makes it harder to read text as it causes your eyes to jump back and forth. You really should do everything that you can to ensure that people can read your work easily, or they will not read it at all.
By the way, this isn't just a hobby or fetish of mine. It's my job.
As for any of your professors who argue otherwise, just let have their email addresses. I'll sort it out.