Projections and propoganda
The Peters projection received a fair amount of criticism. Conservatives charged that it amounted to propaganda, and in fact it was used most often in a deliberate effort to change people’s perceptions of the globe — though, of course, to correct misperceptions created by earlier maps.
A more practical problem is that the Peters projection distorts the shape of the continents far more than Mercator, especially near the poles, so that Canada and Russia appear to have been run through a wringer. All cylindrical projections stretch out the regions near the poles; a cylindrical equal-area projection compensates for that not by removing that distortion but by adding a second one. As a result, it isn’t a particularly elegant solution to the problem of accurately portraying the world. It does, however, maintain the familiar (if completely inaccurate) rectangular outline of the Mercator map.
Improvements and compromises
There are equal-area projections that don’t as badly distort the shapes of the continents, but they require giving up the rectangular map outline. The Mollweide projection, for example, is frequently used when accurately representing area is more important than describing shape — to show global distribution of populations or goods, for example.
When you’re reading a map, then, it’s important to be aware of the projection. What aspects of the map are represented accurately, and which are distorted — and are those choices appropriate to what’s being communicated? Remember, just as there is no perfect projection, there aren’t necessarily any bad ones, either — just bad uses of them.
Several projections at the link.