The distances between the planets are always changing because they’re all constantly orbiting around the Sun. Thus it’s important to be clear about what we mean by “closest”.
For example, at the moment this is being written, Venus is in fact the closest planet to Earth. It is also the planet where the *minimum* distance between that planet and Earth is smallest. We have, at some point, been closer to Venus than we have ever been to Mercury. The map of the solar system you learned in school also remains true. Mercury has the tightest orbit around the sun, followed by Venus, and then Earth.
So in what sense is it correct to say that “Mercury is closest”? That would be average distance. The further a planet is from the Sun, the wider its orbit, and the further away from us it can get when we are on *opposite* sides of the Sun. It turns out that having these periods of being very far away really increases average distance, so the planet with the lowest average distance is the one with the tightest orbit: Mercury. This isn’t even unique to the relationship between Mercury and Earth. When you use average distance, Mercury is closest to *every* planet.
A metaphorical way to think about it is that Earth and Venus are like a married couple. They spend a lot of time in the same house, often right next to each other, but they also have jobs on opposite sides of the city. Mercury is like the shut-in neighbor of this couple who never leaves their house. It is never particularly close to either member of the couple, but when they are at work, it is closer to the couple than they are to each other. The couple works a lot, so Mercury is closer to each on average then they are to each other.
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