Today, colonizing Mars is also "way outside of what is possible". It's all a matter of wanting to do it and then figuring out how to do it, one step at a time.
I'm sure that with enough time and effort we can figure out how to reach the Earth's core. Of course it will take a lot of creativity and lots of people and resources to figure it out, but we can definitely do it.
Also the Earth is right here, we are on it right now. Mars is very, very far away. We can iterate a lot faster here on Earth than anything we want to do on Mars.
What do we gain by colonizing Mars?
We can probably gain the same, or more, and faster, trying to reach the Earth's core first than trying to colonize Mars. In fact, reaching the Earth's core might even make it easier/faster to colonize Mars by applying all the knowledge and tech we would develop.