Question

Why is it impossible to reach the centre of the earth

Answer 1

We cannot reach by drilling.Simply because it's too hot and too much pressure underneath.
Temperatures can go beyond 1000 degrees Celsius. The pressure can be upto 20 Gigapascals. And that's just the mantle.
Now suppose you are drilling with a high temp resistant Tunnel Boring Machine( now human survival at high temp is out of question).
When you start drilling you will find that for every kilometre you drill temperature's increasing by 25 degrees Celsius. After 9-10 kms itself your Machine will not be able to handle the heat.
Let's suppose for the sake of argument that we manage to drill to the mantle, a vertical shaft will cause magma to rise(pressurised magma will look for an outlet).
Then how do we deal with that.
So for that and several other reasons I dont think it's possible to drill to the core.
The greatest depth to which we have drilled is 12 kilometres
However by using seismic waves we can get a basic idea about the different densities of earth layers.

Answer 2

We cannot reach by drilling.Simply because it's too hot and too much pressure underneath.
Temperatures can go beyond 1000 degrees Celsius. The pressure can be upto 20 Gigapascals. And that's just the mantle.
Now suppose you are drilling with a high temp resistant Tunnel Boring Machine( now human survival at high temp is out of question).
When you start drilling you will find that for every kilometre you drill temperature's increasing by 25 degrees Celsius. After 9-10 kms itself your Machine will not be able to handle the heat.
Let's suppose for the sake of argument that we manage to drill to the mantle, a vertical shaft will cause magma to rise(pressurised magma will look for an outlet). 
Then how do we deal with that.
So for that and several other reasons I dont think it's possible to drill to the core.
The greatest depth to which we have drilled is 12 kilometres
However by using seismic waves we can get a basic idea about the different densities of earth layers.