For instance, we don't have a lot of experience with large groups of people in space for that long. We're talking at least 7 months each direction if they're coming back, plus waiting for the return window and executing it. That's an insane experiment in low gravity isolation that by itself hasn't been tackled-- most astronauts are only in space for 7 months at a time on average for a trip, and they need varying amounts of recovery afterward. We're talking about twice that, for an entire crew, plus time spent on the ground on mars in a lower gravity field than here on earth.
Then there's the fact that the crew will need to be large to be sufficiently redundant... and that runs into the problem of having many people in a small isolated space for such a long period of time. I think the largest crews we've had up there were around 10 people. A mars mission would need enough people to prevent everyone from dying if something went wrong on the way there, the wait for the window, and the launch for the return trip, and the return trip itself. I don't think we know how many people that would take currently.
I don't think we can confidently say that it's even possible until we have more experiments studying those things alone.
I'm not at all an expert these are just layman opinions and observations, so if I'm off base I'd like to know. But that's how I understand just the problem of going there.
Challenges of low gravity aside, this doesn't seem that different to a modern submarine. We have nuclear submarines with crews of ~150 that stay submerged for months at a time - the navy has to have some idea how to address the cultural problems inherent in packing 150 people into a tin can...
Why do you think that's an unsolved problem? Genuine question. I thought that part is a straightforward engineering problem. (A very challenging one of course. I'm not saying it's not, just one where we have a lot of previous experience. I never thought that the fundamental possibility of it is in question.)