Why do people think we can terraform Mars?

all I hear is people saying it is impossible or extremely unlikely. Is it really theoretically possible to terraform an entire planet so as to start up civilization there? If we would only be able to live in "domes" as some claim, why do people still want to try to get there? I realize it is only human to want to explore the outerer limtis and never to accept the "impossible" but why is there such a discrepency between people who think its entirley possible to colonize Mars and others who give it an ice cube's chance in hell? Is it possible or not, what's the truth?