Lincoln says that in 1861, "all dreaded it [civil war]--all sought to avert it" (lines 13-14). what reasons does he give in the speech for why war came in spite of these shared feelings against war?

Lincoln reasoned out that there were insurgent agents who were intent on destroying the Union without war but there were parties who would rather wage war and have an easy triumph.

Here is his reason:

"While the inaugural address was being delivered from this place, devoted altogether to saving the Union without war, insurgent agents were in the city seeking to destroy it without war—seeking to dissolve the Union and divide effects by negotiation. Both parties deprecated war, but one of them would make war rather than let the nation survive, and the other would accept war rather than let it perish, and the war came." - President Abraham Lincoln, Second Inaugural Address March 4, 1865. 

They made a checks and balance system to equal power within the branches. the "check" meant that one branch would watch one branch and "balance" them if they were too powerful. if you want more info on this, i would just google checks and balance system.