I guess the simple answer is 'to spread the evil communist agenda'. But what did they tell their people to justify it morally? From their view was it about liberation of the Southerners from American oppression or did they have comrades and sympathisers down South they wanted to team up with like in Vietnam? Was there some covert stuff going on from the American side trying to provoke a war with the North?
You could say Hitler just invaded his neighbours cause he was an evil Nazi imperialist but obviously there was more to it as there was a reason the German people were willing to fight so hard in that War - a mixture of revenge, liberation of German land and citizens as well as Hitler's vision of lebenschraum and a pure aryan Europe. When you consider this about that situation, it must be reasonable to suggest that there is more depth to the situation in Korea as well.
Not looking for a political rant, looking to understand things from a different point of view.
Actually, none of the above! The official North Korean line, both at the time and now, is that North Korea was invaded by South Korean forces (supported both openly and covertly by the American jackals), and that it sought only to defend itself against this naked aggression. In fact, Kim il-Sung's military genius was such that North Korea regrouped, counterattacked, and captured Seoul within three days. Quite the accomplishment, but as you can imagine, the miraculous logistics behind this are not the subject of great scrutiny in North Korean history classes.
Just to clarify, are you only interested in North Korea's official reason for the war, or are you more interested in all of the participants' reasons for getting involved? The tricky thing about geopolitics is that everybody has an "official" rationale for their involvement in something, but that might not be the real reason they're doing it. A state's real motivation will not always be publicly palatable.
Just to add to /u/Cenodoxus answer, it is true that the South attacked the North prior to the start of the war. From the beginning of the division in 1945 both the North and South became increasingly hostile towards each other. The 38^th parallel, which was supposed to be temporary, was drawn without any consideration for the actual geography of Korea and both sides were jockeying for the best positions. On the Ongjin Peninsula, the ROK and DPRK had skirmished a few times in 1949 over their mountain positions. The Ongjin Peninsula was the worst possible place to be for the ROK soldiers. It was separated from the rest of the ROK and when the North Korean attack began, Ongjin was the first place they attacked. The soldiers had nowhere to retreat to but the ocean. Miraculously, most of the ROK 17th Regiment escaped, including their commander, Colonel Paik In-yup. Paik was the younger brother of Paik In-sup, another Colonel in charge of the defenses along Paju, west of of the Ongjin Peninsula. Both brothers would survive the war with In-yup passing away in 2013. Sun-yup is still alive (and 97!). He became the first Korean full General and he led a very distinguished career, helping modernize the Korean military in the 50's and 60's.
But I digress. The point I wanted to make is that the Korean War was not a sudden, surprise attack, at least not as much as people make it out to be. Paik In-yup placed his troops on alert a full 5 days before the war began because he saw troubling troop movements north of his position. He and his troops had traded places with the North Koreans on a few occasions prior to then, and his preparedness was, in part, what allowed him and his men to escape relatively easily instead of being wiped out like so many other front line troops were. That the civilian commanders and the US advisors ignored the warning signs is what made the attack such a "surprise." Had they been paying attention, it would have been obvious.
TLDR - /u/cenodoxus is right, the official line is that the North fought a defensive war and sought to re-unite the country and remove the American puppet masters, but it should be noted that the North and South had fired shots at each other earlier than June 25 and that the South had, on at least 3 occasions, skirmished with the North over positions on the Ongjin Peninsula.
