The desire to collect is innate and probably relates to the gatherer instinct that differs humans from other primates. But in a world in which one can collect everything from antique barbed wire to Victorian pocketbooks, why do people collect stamps? The answer I think comes down to three factors- community, size and orderliness.
First, most stamp collectors were introduced to the hobby by a relative or friend and the feeling one has about philately gets infused with the feelings one has about the early sharing of your hobby with that important person in your life. Second, one can collect at a pretty high level over a period of years and yet store the entire collection on a couple of shelves. Some other hobbies have this advantage, but few have it as clearly as stamps. Most collectibles are far larger and harder to store than stamps. A philatelic collection of thousands can be kept in one album whereas a collection of a thousand horseshoes takes up a garage. This means that a stamp collection can easily be retained during periods of disinterest (which happens with all hobbies) to be picked up again at a high level when interest returns.
And third, orderliness relates to both comprehensiveness and cleanliness. Few other hobbies have catalogs and none are as detailed as stamp catalogs. Knowing what you need is appealing to collectors. And, despite what our spouses say to the contrary, philately is clean and neat compared to most collecting hobbies and fits in well with modern living situations. After all you don't collect classic meerschaum pipes. Just think how wise you were when you decided to collect stamps. You found a hobby that is neat and clean, takes up little room and can be put away for years to be returned to easily and at the same high level from which you enjoyed it before.