A combination of two reasons: 

 - Newton method attracts to saddle points; 
 - [saddle points][1] are common in machine learning, or in fact any multivariable optimization.

Look at the function $$f=x^2-y^2$$
[![enter image description here][2]][2]

If you apply [multivariate Newton method][3], you get the following.
$$\mathbf{x}_{n+1} = \mathbf{x}_n - [\mathbf{H}f(\mathbf{x}_n)]^{-1} \nabla f(\mathbf{x}_n)$$

Let's get the [Hessian][4]:
$$\mathbf{H}= \begin{bmatrix}
  \dfrac{\partial^2 f}{\partial x_1^2} & \dfrac{\partial^2 f}{\partial x_1\,\partial x_2} & \cdots & \dfrac{\partial^2 f}{\partial x_1\,\partial x_n} \\[2.2ex]
  \dfrac{\partial^2 f}{\partial x_2\,\partial x_1} & \dfrac{\partial^2 f}{\partial x_2^2} & \cdots & \dfrac{\partial^2 f}{\partial x_2\,\partial x_n} \\[2.2ex]
  \vdots & \vdots & \ddots & \vdots \\[2.2ex]
  \dfrac{\partial^2 f}{\partial x_n\,\partial x_1} & \dfrac{\partial^2 f}{\partial x_n\,\partial x_2} & \cdots & \dfrac{\partial^2 f}{\partial x_n^2}
\end{bmatrix}.$$

$$\mathbf{H}= \begin{bmatrix}
  2 & 0 \\[2.2ex]
  0 & -2
\end{bmatrix}$$

Invert it:
$$[\mathbf{H} f]^{-1}= \begin{bmatrix}
  1/2 & 0 \\[2.2ex]
  0 & -1/2
\end{bmatrix}$$

Get the gradient:
$$\nabla f=\begin{bmatrix}
  2x \\[2.2ex]
  -2y 
\end{bmatrix}$$

Get the final equation:
$$\mathbf{\begin{bmatrix}
  x \\[2.2ex]
  y 
\end{bmatrix}}_{n+1} =  \begin{bmatrix}
  x \\[2.2ex]
  y
\end{bmatrix}_n
-\begin{bmatrix}
  1/2 & 0 \\[2.2ex]
  0 & -1/2
\end{bmatrix} \begin{bmatrix}
  2x_n \\[2.2ex]
  -2y_n 
\end{bmatrix}=
\mathbf{\begin{bmatrix}
  x \\[2.2ex]
  y 
\end{bmatrix}}_n - \begin{bmatrix}
  x \\[2.2ex]
  y
\end{bmatrix}_n
=
\begin{bmatrix}
  0 \\[2.2ex]
  0
\end{bmatrix}
$$

So, you see how the Newton method led you to the saddle point at $x=0,y=0$.

In contrast, the gradient descent method will not lead to the saddle point. The gradient is zero at the saddle point, but a tiny step out would pull the optimization away as you can see from the gradient above - its gradient on y-variable is negative.

  [1]: https://en.wikipedia.org/wiki/Saddle_point
  [2]: https://i.sstatic.net/EX5lC.png
  [3]: https://en.wikipedia.org/wiki/Newton%27s_method_in_optimization#Higher_dimensions
  [4]: https://en.wikipedia.org/wiki/Hessian_matrix