This monologue on monograms is for men who wear their initials on their shirts, or are thinking about doing so. It's not intended for men who wear the initials of a shirt designer on their shirts, for they are not yet ready.
It's said that shirt monograms were first used by men to identify their shirts in the laundry. At the time most shirts were white and looked alike, so some form of identification was a necessity then just as it is today. After all, when a shirt doesn't have identification, the laundry applies its own mark, and that's usually something fairly unattractive. So monogrammed shirts serve a very practical function, one that is generally available only to men who have shirts made for themselves, as all dress shirt wearing men should.
A monogram of course is a motif made by overlapping or combining two or more letters to form a single symbol (a series of uncombined initials, such as my own initials on the shirt in the photograph, is properly referred to as a cypher rather than a monogram, but most of us fail to distinguish between the two).
Now since a shirt's wearer presumeably knows who he is, we can ask ourselves who an identifying monogram might be intended for if it's not for the laundry. And the only conceivable answer is vanity. Which is why monograms should be placed out of sight, where the laundry can see them but not casual observers. The best location to my mind is inside the collar. Another that's barely acceptable is the lower left shirt front, below where the pocket would be if there was one (and of course there isn't). Initials there are covered by a man's jacket, and if he doesn't wear one all the time he shouldn't have his shirts monogrammed on his shirt front.
There is a reason for this discretion, and it's fairly simple. No-one will ever think less of a man for not having a monogrammed shirt, but there is a significant portion of the population that will think a visible monogram is showing off. Wise men who monogram do so out of sight.