Answer:  It may look intimate to you, but to a dog, it's infintely more polite to offer a modest butt-sniff by way of an introduction than come up boldly face-to-face.   The rudest way you can meet a dog is with direct eye contact.   Human, brought up to meet a glance directly and to extend their hand, don't usually understand the typical canine introduction.  Dogs learn a lot from sniffing a new acquaintance's rear end, because of the scent glands situated there.  As a dog's sense of smell is more than 44 times stronger than ours, it's unsurprising that your dogs will go by it's nose rather than starting up a facial conversation.

If you watch a selection of dogs meeting, you'll notice that some are considerably more polite with their introductory butt-sniffing than others.  A polite, well-socialized dog will approach from the side, sniff briefly, and move on, often approaching the other's face slightly sideways on, making it clear that he isn't being confrontational.  A rude dog will move in intrusively, sniff long and hard, and sometimes even go in for a full inguinal sniff (the polite term for thorough nasal examination of the other's genitals).

A rude introduction doesn't usually pay off, however, most dogs will move away from it, rather than turning slightly to accept an approach face-to-face.  Dogs don't look each other directly in the eye until they are quite familiar, and you'll rarely see prolonged eye contact even with dogs who are good friends.  If you were comparing dog introductions with human ones, then you could interpret the rear sniff as the handshake, the how-do-you-do, and the brief conversation in which you both establish key facts about yourselves, whereas the subsequent nose-to-nose encounter takes things on to the next stage.