Turkey isn't exactly denying the events of 1915. They admit that Armenian died and they also admit that they are at fault, at least partly.
"The governments of Turkey and Azerbaijan deny that the Ottoman authorities attempted to exterminate the Armenian people. The Turkish government acknowledges that during World War I many Armenians died, but counters that Muslim Turks died as well, and claims that the number of Armenian victims has been inflated, and that massacres were committed by both sides as a result of inter-ethnic violence and the wider conflict of World War I."1
As you can read, Turkey acknowledges the death of all these people but aren't willing to admit that they were trying to exterminate the Armenians.
Turkey is afraid of a few things:2
- reparations (monetary or territorial)
- many of the statesmen involved with the establishment of the Turkish Republic were involved with the Armenian massacres
- massacres and expulsions continued after the establishment of the Republic
- damage to national pride and standing in the world
- possible resettlement of an ethnic minority in modern Turkey
I think this answer describes it very well. There's absolutely no gain to accept it.
Let's just summarize they suddenly are saying that it was a genocide. Besides all the facts written in the paragraph before, the immediate question would be "Why now?".
"Why, Turkey, do you know decide to accept your past? There has to be something in your mind!" To understand it better, imagine that you have a friend who insists that he has never done this one crucial fault in your more youthful days but suddenly he says: "Okay, I've done it." What would you think about such behaviour?
The majority has an opinion and the minority doesn't want to accept it. However, even if the minority says that they fucked up, the majority will still stay sceptical. It just makes no sense to the majority why the minority is about to accept their past. Taking this into account, other high ranking politicians would lose their trust in Turkey as it's not obvious to them why they are doing it. (Especially if Erdogan accepts it who, as we all know, is absolutely against accepting it.)
Why is Turkey still denying the Armenian genocide, a century after the fact?
That's the best argument for Turkey. What lies in the past, should stay in the past. After a century, can you really say if it was genocide? Can you do proper research on something that occurred several decades ago? You can try but the opposing party will always say: "No, can't be. Your research must be wrong because we did the same and had another result. Your sources are wrong and can't be determined as trustworthy." You can do research on history but it always has to be objective, and they opposing party will say that the conducted research just isn't objective.
Let's wrap this up: There's no political or economic gain by admitting the Armenian genocide - they could even be harmed in a economic way: reparations. Accepting it could raise suspicion although they really mean it. The suspicion could harm political and economic relationships. In the end, if Turkey still denies it in 200 years, do you think that humanity will still be upset about it? No, because the real truth will be displaced by that what has been spread the most. Nobody will know if it was a genocide or not, especially not in 200 years if the real incident will then be 300 years old.
(Just some afterthoughts: you can read here why it's not possible to determine if the events of 1915 really were a genocide (out of a legal point of view). The legal situation is complex. If you can't fully determine if it was a genocide, can we, as people who say it's a genocide, judge Turkey? Our legal evidence (not scientific evidence) is contradictory. If we can't solve the legal situation, this will be unsolved forever, literally.)