Short answer: marketing.

Long answer:

OK, first let's go over what light beer is. You can't make beer out of normal grain because most of the carbohydrates in grain are too complex for yeast to eat and if yeast can't eat something then they can't change it into alcohol. As part of the brewing process you malt (let the grain germinate a bit) and then mash (cook the grain in water at a very specific temperature range). Malting and mashing break down many of the starches in grain into maltose which is a simple carbohydrate that yeast can eat.

However, malting and mashing do not convert ALL of the carbohydrates in wort (wort is the liquid that you turn into beer by adding yeast) into things that the yeast can eat. This is why there is sweetness in beer, a sweetness that is generally balanced by the bitterness of hops. However, if you add the right enzymes to the wort then you can break down a lot of the leftover carbohydrates into things that yeast can eat.

That way you get less carbohydrates and more alcohol out of the same amount of grain. Or to look at it from the other side, it lets you use less grain to produce the same amount of alcohol and also less hops, because light beer is so dry there is very little sweetness that needs to be balanced with hops. Also by being so dry there is less chance of a light beer spoiling. So from the point of view of a brewer, light beer is wonderful. Although the industrial process to make it can be pretty finnicky (the sorts of brewing flaws that you would never notice in an IPA can ruin a light beer), making light beer needs less in the way of ingredients compared to normal beer.

Modern American light beer is not necessarily that low in alcohol, which makes it stand apart from older forms of lighter beers such as small ale or more modern light ale or boy's bitter which were basically normal beers just weaker in every way (very much including less alcohol).

But the problem was how to make people buy this.

In 1967 a chemist working for Rheingold Brewing company named Dr. Joseph L. Owades made the first recipe for American light beer. It was called Gablinger’s Diet Beer and was marketed as, well, a diet beer. It failed miserably. Dr. Owades was then given permission to share the recipe with the Meister Brau brewery which went on to produce Meister Brau Lite. It was also marketed as a diet beer. It also failed miserably. Meister Brau then went bankrupt in 1972 and was bought out by Miller. Miller relaunched Meister Brau Lite as Miller Lite.

But, because the bosses at Miller didn't want Miller Lite to fail miserably they hired the New York ad agency McCann Erickson. McCann Erickson had some people who were good at their jobs and they did some market research and found that selling light beer as diet beer was a bad idea. When people are drinking beer they're generally not thinking about their health and it's hard to get Americans to buy diet products at the best of times. So McCann Erickson decided to come at it from another angle: if a beer has less carbs in it then it's less filling. If it's less filling you can drink more without feeling full. If you can drink more without feeling full then you can drink a lot of beer. "You can drink a lot of this beer!" was a much more appealing message then "this beer has less calories." They put together some effective ads like this one: www.youtube.com/watch?v=U5APOrMribc As you can see calories are mentioned, but they're not really the focus of the advertisement.

This marketing campaign worked very well, Miller Lite took off and other breweries scrambled to keep up and made their own light beers and the rest is history.

Also, a very very cold light beer can be very refreshing when you're dehydrated, overheated, and tired in a way that no soda is. Anything sweet (artificial or not) isn't what I want if I'm really thirsty. Personally, I just drink water if I'm really thirsty but I can see the appeal of a light beer after mowing the lawn. Also I'm hardly going to slam down an IPA if I'm feeling really thirsty and those don't taste their best very cold anyway.