In 1913 Hitler left Vienna for Munich, partially to escape being called up to the Austrian military service, something he had been avoiding for four years and was loath to serve in because as a pan-Gemanist he despised the multinational Hapsburg empire. EDIT: this is the 'why'. In his youth Hitler had become an admirer of radical nationalist thinkers who believed that all Germans should be united in one state. His experiences in Vienna had strengthened that belief as he came to despise the other nations of the Austrian empire. When war came he wanted to fight for Germans only.

As an Austrian citizen Hitler shouldn't have been able to enlist in the Bavarian army when war broke out. He has a story in Mein Kampf about petitioning King Ludwig III to be allowed to serve and getting approval the next day but as it involves a lightning-quick bureaucracy Kershaw doesn't find it credible, and it seems likely that Hitler just slipped through, as the system was overwhelmed with volunteers. An inquiry by the Bavarian government in 1924 couldn't determine how Hitler was able to enlist, and concluded that he likely wasn't even asked about his citizenship.

Source: Kershaw, Ian Hitler 1889-1936: Nemesis, 1998