Well, Ulrich von Jungingen was too quick to push the war button, indeed (he was a fool, his older brother, who was Grand Master before, even specifically stated in his will that he was NOT to be elected Grand Master), but the reasons behind the war were instigated more by the Poles and Lithuanians.
The Lithuanians were supporting a revolt in Samogitia, which had been given to the Teutonic Knights years before, and thus was an internal problem (so Lithuania should have stayed out of it). Poland threw in their support to Lithuania, whose leader was now linked to the Polish court after his conversion. Poland was also eager to reclaim Danzig/Gdansk....but seeing how the Teutonic Knights took Danzig from the Holy Roman Empire on the behalf of Poland with the intention of payment, it is not surprising that they decided to keep the city when Poland refused to pay and just wanted the Teutonic Knights to hand the city over.
So, despite the fact that modern thought sees Tannenberg/Grunwald as a great Polish/Lithuanian victory over an oppressive Germanic regime....the reality is that the Germanics were not evil in the battle's setting and should not have such a popularity amongst the Poles as some sort of anachronistic vengeance for 20th century events when the motives and reasons are gray all around.
Sorry, I feel strongly about the unfair bad rap the Teutonic Knights get regarding this battle and its reasons.