Jesus directly calls those to whom He was speaking "evil"! Apparently, they were just ordinary people listening to Him teach; they were not representatives of any of those groups that were constantly disputing with Him. Verse 1 suggests His audience was made up of His own disciples! Yet, there is no equivocation at all in His statement. Evil is synonymous with "diseased," "hurtful," "calamitous," "derelict," "vicious," and "malignant." The word derives from the Greek word for "labor," indicating it is something that is worked at, thus producing these evil effects.
In Matthew 19:16, Jesus Himself is called "good," but He promptly corrects the person, saying that only God is good (verse 17). He presumably said that because there were elements of human nature in Him by virtue of His human birth. Luke 11:13, then, is God's assessment of human nature: evil. Just because a human knows how and actually does some good things - acts of kindness or generosity - does not alter the fact that his heart is still incurably evil. Human pride tends to blunt God's assessment of the carnality within us, motivating any remaining enmity (Romans 7:14-24).
Our pride rises to defend us from the condemnation of the standard to which we are compared - God. We consider Adolph Hitler to have been utterly evil, but he is said to have cherished children and dogs, a trait we would tend to judge as good. In a similar vein, James 3:9-10 says that with our tongues "we bless our God and Father, and with it we curse men, who have been made in the similitude of God. Out of the same mouth proceed blessing and cursing." Where do those words come from? Do they not proceed out from an evil heart (Matthew 12:34)?
People judge human nature to be a mixture of good and evil, but that is not acceptable for life in the Kingdom of God! It may as well be totally evil! Is God Himself contaminated, a blend of good and evil? According to I John 3:2, in His Kingdom "we shall be like Him." We will be purified and uncontaminated as He is. Human nature's evil mix will not be seen in God's Kingdom.
We should by now realize that salvation can only be by grace. Human nature not only cannot be made good, but even now it resides just under the surface. Our conversion barely covers it over, as Peter's outburst against God's will illustrates and Paul's experience, reported in Romans 7, amplifies.