The biggest problem is that people have really lost the ability to think big. There's always infinite reasons to not do something, and there will never be a perfect time. So at some point you simply have to choose to push forward. Like Kennedy put it:
"We choose to go to the moon. We choose to go to the moon in this decade and do the other things, not because they are easy, but because they are hard, because that goal will serve to organize and measure the best of our energies and skills, because that challenge is one that we are willing to accept, one we are unwilling to postpone, and one which we intend to win, and the others, too."
Talk about hyperbole.
The moon mission has been prepared for before that speech took place. It wasn’t just starting from scratch and hitting the moon in 7 years, instead the speech was more public disclosure of a deadline that looked achievable but would hit after his presidency (1960 + 8 being less than before the decade is out: 1970).
The biggest problem is we already did the easy stuff. Playing tag with the moon is unbelievably easier than a permanent moon base or landing on Mars and getting back to earth.
Saying we'd be on the Moon in 7 years was not something that looked achievable except to the most fanatical of enthusiasts. To the average layman it would have sounded no less impossible than me saying we'll have a man on Mars in 7 years from today. And landing on Mars in many ways will be much easier than the Moon. Not only is the terrain broadly more hospitable, but you have an atmosphere to enable aerobraking which simplifies both landing and braking and enables various options (like some sort of parachute staging or backup). The biggest and really only complexity with Mars is its distance. Outside of that it's easy mode.
That’s a meaningless yardstick here. People at NASA definitely thought hitting that target was achievable before the speech.
> Landing on Mars
Landing isn’t the issue. Get people there alive and having enough deltaV to get back is.
It was a mission they dedicated themselves to, and humans have this way of making things happen when we actually set our minds to tasks. A reality that's often been lost in modern times as we have mostly moved away from pursuing, let alone achieving, great things in the real world. One of the many reasons to get humans on Mars.
[1] - https://ntrs.nasa.gov/api/citations/20190002249/downloads/20...
Again, I’m addressing the point “getting them there alive”. Unquestionably, we know how to get crew to Mars alive, and even for the full mission duration, radiation isn’t even in the top 10 of the hazards that could actually kill them during the mission. (It’s a long term hazard, comparable to lung cancer if you’re a cigarette smoker.)
It’s possible people spending significant time on the surface of mars would recover, but that’s more speculation than proven.
Note that the magnetic field only deflects lower energy galactic cosmic rays which have a lower gyro radius than the real whoppers. The magnetic field is less important to overall radiation shielding than the earth’s atmosphere.