On that same note, some people find comfort in the idea that God doesn't change in a world that is always changing. Either point can be argued equally well. "Unchanging in his love" seems to relate to the attribute of immutability. Again, it also explains that God does not change. Most people, who think of an immutable God, think of someone who cannot change in His essential being. Some people hold onto the belief that when we worship God, we are not worshiping a God that is a little better today than He was yesterday. The concept of God being immutable is that He is the same in His being as He is in His attributes.

God's immutability also means that He is immutable to His own will, as well as in His plans and purposes. A good example of this is...

Most people believe that God is perfect and that His plans are perfect, thus He does not have to reason with Himself and never changes His mind, but this isn't entirely accurate or realistic either. Again, if God molded this world after a world he knew or himself, it is safe to say that He can change His mind and many often do so. This thought comes from the fact that the world is ever-changing and most people have felt at some point in their life that fate has been changed for them.
Still, most people prefer to believe that God is immutable, or perhaps they hold onto the idea that there is still something in this world that will never change and is never wrong, no matter what.