What evidence is there to call the 1919-1920 conflict between Poland and the Soviet Union a "war of independence"? As for a definition of independence, I would say it is a full political, legal, and military independence from another state -- for example, a vassal becoming independent in a war. Note this is based on a comment on this answer.
If Germany decided to invade Poland to get back East Prussia that it lost to Poland after WWII - would it be a war of independence?
One needs a lot of fantasy to call the Polish–Soviet War (this seems to be the official name of the conflict) a war of independence. In 1919 Poland was already independent - it gained its independence with the Treaty of Versailles. The issue was rather that Poland wasn't satisfied with the territories it gained and would like to recover all the territories it lost in the partitions. This meant first suppressing the Ukrainian independence movement in the Western Ukraine (Polish-Ukrainian War). But given that Western Ukraine had a large Polish population one could still explain it with defending the newly born Polish state.
This explanation no longer works for the Polish invasion of East Ukraine and Belarus in the course of the Polish-Soviet War. While these territories historically belonged to Poland (they changed hands a number of times actually) they didn't have a significant Polish population. So this had nothing to do with independence. Instead, there were quite obvious strategical reasons:
And while time proved that Poland's fears weren't unfounded (Poland was once again occupied by Germany and Soviet Union in 1939) - it was a war over territory and power, not independence.
The Polish-Bolshevik war (as it is known in Poland, I believe rest of the world use term Polish-Soviet war) is not known as the war for independence. After all, Poland re-gained independence on November 11, 1918 - when I World War ended (which was later confirmed by the Treaty of Versailles).
As for causes of the war you are asking about, as always there are few. I strongly believe, on one hand it has something to do with distrust between Poland and Soviet Russia (Polish politicians simply thought the Russians want to gain some time and their peace treaty offer is not real.)
Personally, I don't think it was fight for Great Poland, or re-born of Polish-Lithuanian Commonwealth, it was rather preventive war.
Although, I might be wrong - given the facts like annexation of Vilnius Region and annexation of Zaolzie, Second Polish Republic was fairly aggressive and who knows what Piłsudzki and his friends thought...
In my opinion, a "war of independence" is war where the very independence of a newly born country is at stake. There is no question that if Soviet Russia won the war with Poland in 1920, Poland would lose independence, which it barely gained a short while before. Therefore, from the Polish POV it was a "war of independence".
Going back in time a little, the Polish-Ukrainian offensive of early 1920 was meant to safeguard Polish independence by creating independent Ukraine under Petlura, and therefore it can also be considered a part of "war of independence".
It was indeed a war of independence that was played out within the larger context of the First World War, the 1917 Russian Revolution and subsequent Russian Civil War.
Poland had been conquered by Russia during the 19th century but Polish identity and nationalism never died. Recognizing this, the Germans hoped to win away the support of the Polish people from Russia during the First World War by aiding Polish aspirations for independence in 1916, albeit in a heavy-handed manner.
After the October Revolution, Vladimir Lenin felt that a great revolution would sweep Europe and Germany was seen as the ideal epicenter. That drove the Bolshevik desire of advancing the revolution with its Red Army into Germany and to do so, it had to advance across Poland, both politically and militarily. Polish independence goals, captured in the ideas of Josef Pilsudski, envisioned a "Greater" Poland that included Vilnius and the western Ukraine. Those conflicting Soviet and Polish objectives made the conflict inevitable in 1919.
By the way, unpublished (secret) articles in the 1939 Soviet-German Non-Aggression Pact dealt with the invasion and partition of Poland between Hitler and Stalin. According to the research of Dr. Stuart Goldman, The Red Army did not cross the Polish Frontier until 17 September 1939 because Stalin had to remove the threat of the two-front war by resolving the conflict with Japan over Nomonhan in Outer Mongolia, which was not completed until 16 September when a ceasefire went into effect.
When the Soviets invaded, the British and French seized on technicalities in the language of the military alliances with Poland to avoid going to war with Stalin, acts that may have been dishonorable, but in reality, they had no rational choice. Hitler then betrayed Stalin and attacked the Soviet Union in June 1941, sealing the fate of Nazi Germany.