Excuse me for being human
An example of one of the many euphemisms used to politely, or at least colorfully, excuse oneself to perform necessary excretory functions.
The list is long and colorful. I offer a small selection of euphemisms with the firm expectation that you have encountered a few of them yourself.
As you may observe, the descriptive terms quickly exit names for the room and instead deal with the functions themselves. The names for the room where elimination occurs uses everything but the term urination or defecation.
We go to the John, the lavatory, the bathroom, the loo, or the restroom. There is a social stigma attached to these normal bodily functions that language seeks to work around without undue embarrassment. Perhaps it is a holdover from Elizabethan times when men and women sought to deny their grosser nature. After all, a proper lady could hardly be thought to poo, much less reel off a hot coil.
Anyone familiar with small children, and especially little boys, will recall their fascination with these bodily functions. Parents have wondered eternally if their offspring will outgrow this fascination or simply become a testimony to the shallowness of their
gene pool. What a relief when the little angels find a different subject to spellbind them, such as how many
Oreo cookies they can put into their mouth at once.
Considering the extreme measures employed to avoid plain speaking about the goings-on in the 'necessary room', it's little wonder we have such little success with other things such as world peace. To call a spade a spade, it's a pantload.
Another explanation
Another take on the phrase 'see a man about a dog' has a broader application. It is employed when to reveal the true reason for one's absence might prove embarrassing. The phrase has been used to mask going to see one's bootlegger during prohibition, to hide a romantic assignation, or other equally risky act. Rather than give a specific (and truthful) explanation, it is easier to offer the time worn phrase. The usage of going 'to see a man about a dog' creates suspicion in and of itself. To offer up this chestnut reeks of bull crap, which once again brings us full circle in our excretory circumnavigation.
Sources:
http://www.wisegeek.com/what-are-some-common-euphemisms-for-the-bathroom.htm
http://www.grupthink.com/topic/405
http://azargrammar.com/grammarGuy/2008/07/rose-by-any-other-name.html