But then we have Venus, which also has no magnetic field, yet has the densest atmosphere in the solar system. It is so dense, the pressure at the surface is 92 times greater than Earth. Venus is only slightly smaller than Earth, has about the same mass and gravity, and is thought to have had oceans at one time. However, while our atmosphere is mostly nitrogen and oxygen, the Venusian atmosphere is 97% carbon dioxide and 3% nitrogen with a few other trace elements, including water vapor. This has caused an extensive runaway greenhouse effect which, if there were oceans there, caused them to evaporate. And it's hot. Damn hot. The surface temperature is 460° C (860° F.) Even if Venus were to move into the habitable zone, there is insufficient water to condense even if the planet were able to cool enough, which is doubtful anyway due to the massive amounts of CO2.
Mars, on the other hand, is much smaller than Earth. It's radius is only slightly more than half of Earth's and it's mass is only about 10% of our planet's, making it's gravity much weaker. If it ever had a dense atmosphere, it is probably for this reason along with the lack of a magnetic field, that it was lost to space. It's atmospheric make-up is quite similar to Venus with carbon dioxide making up 95%, nitrogen 3%, argon 1.5%, with several other trace elements including oxygen and water. Compare that to Venus and it is almost identical except that Mars' atmosphere is much more tenuous. The atmospheric pressure at the surface is only about 1% of Earth. However, it does have seasons much like Earth. The temperatures range from highs of around -5° C (23° F) in the summers to -87° C (-125° F) in the winter. The average mean temperature is -63° C (-82° F.) It has polar ice caps which are probably water ice and it is possible there is a substantial amount of subterranean water. If Mars were to warm sufficiently to melt the ice caps and bring the underground water to the surface, it is possible that the atmosphere could once more thicken and inject enough oxygen and other essential elements for human survival. It is even hypothesized that Mars could be purposefully terraformed to support human life.
Another factor that comes into play is a planet's rotational rate. Mars has a rotation similar to Earth. It's day is only slightly longer than Earth's, meaning each side of the planet faces the sun on a regular basis. Venus, on the other hand, rotates so slowly that it's year is actually longer than it's day. It takes approximately 225 earth days to orbit the sun, yet it takes 243 earth days to rotate once. This has contributed to the massive greenhouse effect to the point that the climate is geothermic, meaning temperature doesn't vary from the day side to the night side or from the polar regions to the equator. (Just as an aside, because I find it interesting, Venus also rotates backwards from most of the other planets. This is probably due to a massive collision with a large body which literally turned the planet upside down. And I say most others because Uranus is turned on it's side with one of it's poles pointed towards the sun and basically rolls along it's orbit.)
All this is to show that there are many factors involved in what can make a planet habitable as we define that condition. Venus, which is between the habitable zone and the sun, has a runaway greenhouse effect and is extremely hot. Mars, which is on the other side of the zone, has only a thin atmosphere and is very cold.
What if their positions had been reversed? We can speculate that Mars would be like Mercury, the closest planet to the sun. It has an atmosphere slightly thicker than Mars, and although smaller than Mars, is denser and has more mass, so the gravitational field is about the same. But then it does have a magnetic field. Had Mars been on that side of the habitable zone, it would have naturally been much warmer, but whether it could have retained a thicker atmosphere would depend on many factors. Did it ever have a molten iron core to produce a magnetic field? If so, would being closer to the sun keep it molten? Would it's weak gravity have caused it to loose it's atmosphere anyway?
If Venus were in Mars' position, the atmosphere would probably be cooler, but with it's make-up, would it be cool enough? Carbon dioxide is a notorious greenhouse gas as we know due to our current experience here in Earth with global warming. If oceans ever did exist there, the atmosphere could have been much different. We know that the atmospheric make-up of Earth has changed since its formation, so perhaps the Venusian atmosphere could have supported life as we know it had the planet been in a different location.
I do agree with you and others that the scope of what we consider a habitable environment is narrow, but since the conditions in which we live are the only ones we know, that is to be expected. That is why I interject the phrase "life as we know it" when talking about the possibility of life elsewhere. Who knows? We may someday find that life can exist in conditions other than our own.