I heard Jerry Pournelle talking about this and he said something like landing a man on the Moon and establishing a lunar colony is an engineering problem. Landing a man on Mars is a science problem.
The difference? We can already do the former. it's simply a question of money and the will to do it. The problems are basically solved.
Landing a man on Mars has far bigger problems. The round trip (or even one way) journey with current propulsion technology will take an incredibly long time (upwards of 2 years). How do you keep someone alive that long? What about the psychology of isolation? Sustained radiation exposure is a real problem.
Personally I see manned spaceflight, particularly to other planets, as being largely a propaganda exercise until:
1. The cost of lifting into orbit (per kg) goes down. Way down. Like 2 or even 3 orders of magnitude; and
2. We have a much faster means of propulsion to make journey lengths manageable.
(1) is probably the easiest to solve. SpaceX's launch prices are actually quite low (but those are fairly low orbits; launching to another planet is more expensive). Virgin Galactic and other private suborbital efforts will (hopefully) lead to a dramatic cost reduction of getting into orbit.
(2) is a fundamentally hard problem. Ideas such as solar sails and the like are far from being practical (plus with a solar sail, how do you get back?). Magnetic fields as solar sails is an interesting idea but has a whole bunch of other problems.
Otherwise you need to eject mass to give you velocity. That mass is something you have to carry. The more mass (fuel) you carry, the less effective each gram is (in delta-V terms).
What I think will probably drive this is the coming earthbound resource shortages (inevitable unless we drastically reduce population; it's simply a question of when) that will drive a permanent presence in space. Once you have a huge industrial manufacturing capacity in space, the economics completely change.
EDIT: I agree with other comments in that a one-way (colonization) mission makes far more sense but I'm still unconvinced this will happen anytime soon, probably not in my lifetime.
Mars does have some interesting properties though if a colony can become self-sustaining:
1. Lower gravity. This actually makes the idea of a space elevator far more feasible [1]; and
2. Mars has features that extend beyond the atmosphere. The atmosphere is ~11km thick. Olympus Mons is 25km high.
I've read seemingly informed speculation that if we (the human race) had evolved on Mars, we'd already be heavily spacebound since it would be far, far easier.
This is what might justify colonizing Mars. Not that that is an easy problem.