It's less a matter of why, more a matter of where and how.
Dragons are honor bound to give their enemy a fair fight. This doesn't necessarily mean one-on-one: in the case of a very powerful dragon, multiple opponents are acceptable. Dragons are also required to issue a challenge and give the other dragon an opportunity to retreat. This requirement is waived if the two dragons meet in third-party or neutral territory, i.e. territory of an uninvolved or neutral dragon, or unclaimed territory. However, most dragons continue to honor the retreat rule even under these circumstances.
Once the challenge is given, if the other dragon doesn't retreat it become a fight to the death. There is no shame for a dragon in refusing to fight a superior foe, and there is little pride for a dragon in killing an enemy who doesn't stand a chance against them. Under very rare circumstances, a dragon may allow a defeated foe to live, though dragons consider this humiliating unless the fight becomes a draw.
There are a few laws dragons are expected to follow with regards to killing each other--
Trespassing: Dragons are required to respect the territory of another dragon, and as such should ask permission before spending more than a few days in another dragons territory; most will even inform the dragon if they are just passing through or visiting, but this is a matter of etiquette. Trespassing isn't cause for death unless the other dragon invades the others lair or refuses to leave. Dragons are required to give the offending dragon a warning, which can (and often does) involve physical violence right up to the point of death. If the offending dragon stays, or returns without permission, the aggrieved dragon may kill the offender without giving them another chance to retreat. The thinking here is that the offender forfeited his right to retreat when he stayed or returned without permission. If one dragon decides he wants some (or all) of the territory of another dragon, he can offer to barter or try to take it by force. If the aggrieved dragon retreats, the offending dragon gets the contested territory. A weaker dragon might relent over a smaller piece of land, but it is unlikely that any dragon will abandon all their territory, even to an enemy they can't possibly defeat. In this circumstance, the offending dragon is usually considered in violation of dragon honor by attacking an opponent who has no fair chance, and by putting him in a virtual "no retreat" situation.
Spawning: Dragons only have sex in their natural form when they wish to reproduce, and this only occurs when a male dragon enters a state called breedlust. In this state, the male dragon takes off and looks for a mate, and doesn't think about much else. If a female dragon is interested, she can activate her ovulation and attract the male. This is the only circumstance under which dragons will have sex in their natural forms. They view reproduction as sacred, and will not defile it for pleasure. Sex between dragons in human form is fine, however...so is sex with humans (though some dragons find it tacky). It is rare, but occasionally two males will be overcome with breedlust over the same female. The normal rules of challenge apply here, and the weaker dragon usually relents and moves on to find another female. It isn't common for dragons to actually fight over a mate, since the odds of two dragons of equal relative power meeting over a single female are very low.
Infanticide: Dragons reproduce infrequently. As such, mother dragons are very protective of their egg. Damaging an unhatched egg in any way is the worst crime any dragon can ever commit. Most dragons won't even consider the possibility, and are offended by the mere thought of it. Only slightly less heinous is killing a hatchling dragon (100 yrs. or less). For the first century or so of life, the hatching lives with it's mother and learns to be a dragon from her. Dragons do not participate in fatherhood under normal circumstances, and most dragons have no idea of who their father was. If a mother is killed, the victor is responsible for seeing to the safety of the fallen dragon's egg or hatchling. Dragons consider caring for the young of a fallen dragon mother one of the highest honors they can be asked, so it usually isn't difficult to find someone to raise the hatchling. In very rare cases, a male dragon may adopt the spawn of a fallen mother. These are the few unusual instances of a dragon having a father, but not a mother. It isn't against the rules for a dragon to adopt the spawn of a mother dragon they have killed, but it's considered awkward.
Personal assault: An unprovoked attack against a dragon or anyone the dragon has chosen to serve (usually another dragon, rarely another creature like a human lover) is grounds for the aggrieved dragon to kill another. They are not required to issue a challenge or allow retreat in this situation, but most will out of etiquette--though they will usually require some form of restitution for the slight.
If one dragon kills another, he gets the other dragons horde, lair and territory. He does not gain the loyalty of any dragons or creatures who served the fallen dragon, unless they wish to give it--they usually don't. As for how dragons can kill one another, dragon honor allows only physical combat. Use of sorcery, technology, traps, or any other means is considered dishonorable. In grievous instances, the Echelon may even forfeit the winnings and pass them on to another dragon. In most cases, the loss of reputation and honor is sufficient punishment, unless the dragon uses such tactics repeatedly. If a dragon has the loyalty of another dragon, it is permissible to have them fight in the master dragons stead. In fact, this is generally how very powerful dragons choose to deal with opponents too weak to be an honorable fight: they send a minion of approximate power. Honor dictates that this minion be a dragon. Sending another creature is an insult, kind of like mocking your opponent in a car race by showing up in a wheel-barrel. Even if the minion is of sufficient power to fight the dragon (like a very powerful demon) it's still pretty offensive.
These rules only apply to dragons killing dragons. They don't have any such rules with regards to other creatures or opponents, but many dragons will honor the rules with them out of habit or tradition.
One final exception: if the Echelon decrees--by majority vote--a dragon to be anathema, they can be killed by any dragon, any time, any where and in any manner. The subject of this decree is no longer considered a dragon, so rules of honor no longer apply. Any dragon who aids or protects the anathema is considered to have willingly forfeited his or her rights under dragon law and can be similarly killed. This is epically rare, however, and usually reserved for the worst of the worst. As one would expect, dragons declared anathema don't survive for very long so what few of them there have been aren't around anymore.