Question

Disadvantage of neural network according to your purview is

Answer 1

Here are several disadvantages that I can think of off the top of my head:

Long training times for deep networks, which are the most accurate architecture for most problems. This is especially true if you're training on a CPU instead of a specialized GPU instance.
Need lots of data, especially for architectures with many layers. This is a problem for most ML algorithms, of course, but is especially relevant for ANNs because of the vast number of weights and connections in ANNs.
Architectures have to be fine-tuned to achieve the best performance. There are many design decisions that have to be made, from the number of layers to the number of nodes in each layer to the activation functions, and an architecture that works well to some one problem very often does not generalize well.