I don't know what radio program you were listening to, so I'm not sure whether the person speaking was a doctor/scientist, or a statistically illiterate crank. It's possible that he was looking at valid scientific projections for maximum age, but he probably just misinterpreted the historical statistics on longevity.

One important thing to note is the distinction between life expectancy and life span. Life expectancy is the average number of years every person, at birth (unless another age is given), can expect to live before dying — in developed countries, this is usually in the 70s. Keep in mind this is an average, and it factors in many people who die in infancy and early childhood. Life span is the number of years a person actually lives, with maximum life span (this is what I assume you're talking about) being the maximum number of years a human can possibly live.

Life expectancy, of course, has changed dramatically over the past 100-200 years. In the U.S., for example, the average life expectancy per decade increased like this:

1900: 49

1910: 52

1920: 56

1930: 59

1940: 64

1950: 68

1960: 70

1970: 71

1980: 74

1990: 75

Source: E.F. Moody

For the entire world, the increase has been even greater. But there are several factors that go into this. Yes, people are "living longer" in the sense that better medicine and better health practices have helped people die from "natural causes" at later ages. Today's 70-year-old is more likely to reach 80 than in years past. But the world life expectancy numbers have also shot up because fewer and fewer children are dying in infancy. Remember, life expectancy numbers are given from birth. A child dying at 12 instead of 2 will change this statistic just as much as a great-grandmother dying at 90 instead of 80.

Consider a hypothetical population of 1,000 people, where 500 of them die before their first birthday, and 500 live to be 100. What's their life expectancy? It's 50 years, even though nobody is expected to die at age 50. In fact, a 5-year-old has a 100% chance to reach 100.

So knowing that the life expectancy on planet Earth has risen from (for example) 60 to 70 does not necessarily mean that our elderly population is getting older than before, or that everyone can expect to live an extra 10 years. It might just mean that we're not dying young anymore. If all disease, war, natural disasters and accidents were wiped out, the human life expectancy could rise to something over 100. But that doesn't mean that humans, as a species, would be able to live longer and longer. It just means that they would be more likely to reach their maximum life span. It's a subtle but important difference.

Based on the statistics we have now, the human life span seems to max out around 120 years. The oldest person in documented history (unless you take the Bible literally) was "only" 122 when she died. More and more people are reaching 100, but they're not going much further. There's no clear evidence that the "age ceiling" is moving. If it is, it isn't increasing nearly as fast as life expectancy.

To reiterate, the maximum life span of human beings hasn't changed (or hasn't changed much) — we're just becoming more and more likely to reach it.

With that in mind, I suspect that your radio guy might have simply looked at life expectancy rates on an upward-curving graph to make his predictions. As you have seen, this is a very faulty way of looking at the reality, but if you want me to construct a bogus "mathematical proof" anyway, I think I can do it:

Let's say that between 1900 and 2000, world life expectancy at birth grew from 35 years to 70 years (a close enough approximation). We can look at this number and say, "Hmmm... every 100 years, life expectancy doubles." By that reasoning, life expectancy at birth in 2100 would be 140; in 2200 it would be 280. If we also assume that the record-setters will live four times longer than their life expectancy at birth (the 122-year-old woman was born in the 1870s, when life expectancy was probably around 30), a future 200-year-old is no doubt alive today. And the future 1000-year-old would be born whenever the average life expectancy reached 250 — or sometime in the late 2100s. Since that is less than 200 years in the future, our 200-year-old and 1000-year-old would overlap. There. I "proved" it.

OK, taking tongue out of cheek, there has been a lot of research in the area of aging recently, and scientists seem to be close to discovering how to actually slow the aging process. This would result in actually moving the age ceiling to 130 years, or 150 years, or possibly 200 years. And then — who knows? — we might even approach immortality. But at this point, this is all just a dream. Someone may have projections for how fast maximum life span will increase, but based solely on the historical record, there's no reason to think it will go much past 120.

Sources: The Longevity Meme, Can You Live Forever?, Community Science Action Guides, E.F. Moody, Human Immortality: A Scientific Reality?, The Case Against Aging