In all honesty I believe both parties want the same results but they disagree on how to get there. You'd be hard pressed to find a liberal or conservative who didn't want better education for their children, home ownership, safe neighborhoods, a growing economy that provided decent paying jobs, and an opportunity to retire at some point without financial worries.
The primary difference in their ideology concerns how much the government should be involved in facilitating these goals into reality. Liberals tend not to trust entrepreneurs and the free enterprise system to address these issues nor do they have faith that the "average person" would do what is in their long-term best interest. They want the government to provide a "safety net" or floor.
One such example is Social Security. Many conservatives believe people should have the option to participate in the program or be allowed to invest those funds in the stock market. Liberals on the other hand point to the "Great Recession" when GM stock dropped to $2 a share as a reason why the average person should not bet their retirement on the stock market. They prefer a guaranteed fixed income for seniors.
One group wants the government to play the role of "Robin Hood" in an attempt to "make life fair" and the other group believes it's an "eat what you kill world" and the government should get out of the way.
In the end most people vote according to their "pocketbook" needs in addition to "social ideology" that resonates with them.
For the most part it's a waste of time trying to "convince" someone to jump sides. Much like religious debate people have to come into things on their own accord. Otherwise their ego won't allow them to concede they may be wrong.