A connected, simple, 3 regular graph is 2-connected

Question

I understand intuitively that it needs to be the case but don’t know how to prove it. In fact, I think it can be done through a contradiction. We assume G is not 2 connected. But not sure what to do after that, help? Also please consider me a newbie. Be intuitive and concise plz

Answer 1

Take three copies of the graph shown below, and identify the three points o to a single vertex; the resulting graph on $16$ vertices is connected, $3$-regular, and not $2$-connected: removing the vertex o disconnects it.

                 o
                 |
                 *
                / \
               /   \
              *——*——*
               \ | /
                \|/
                 *