Sorry, But Every Map Is Lying To You
Picture a map in your mind. Chances are good that the map you've imagined is the Mercator projection, since it's the most popular. How big is the United States compared to Russia? Greenland to Africa? Antarctica to Europe? If you cross-check the sizes of those countries with those on a globe, you're likely to be surprised.
One of These Things is Not Like the Other
Though the Mercator projection makes Africa and Greenland appear roughly the same size, they're nothing close: Africa is actually a whopping 14 times larger than Greenland. So why do they look so similar on a map? It's because a sphere is not what mathematicians call a developable surface, or one that can be flattened onto a plane without being distorted. For a cartographer to put the globe on a flat surface, sacrifices must be made.
In the case of the Mercator projection, we sacrifice relative size for compass accuracy; that is, the map exaggerates the size of countries as they get closer to the poles, but maintains true north-south and east-west direction between any two points to make navigation easier.
Other maps might show more realistic sizes but make trade-offs in continuity or distance. Even using a globe has its drawbacks: you can't see every country at once, and it forces you to measure distance in arcs instead of straight lines.
Japanese architect Hajime Narukawa believes he's developed the most accurate map so far. It's called the AuthaGraph World Map. This version divides the world into 96 triangles, making it a tetrahedron, then unfolding it to become a rectangle. This preserves the true dimensions of the continents by angling them outward instead of stretching them. Narukawa admits even his map is not entirely accurate yet — some regions are slightly distorted.
If you want to get a better grip on how big your homeland is, check out this online tool that allows you to drag various countries around a map. You'll see that the size changes, depending on what you're comparing.
In the end, the most "accurate" map depends on what you'll use it for.