Is it a sin to ask God "why"?

In the disappointments of life, is asking "Why?" appropriate?

Yes. If we want to benefit from our experiences, we need to learn God's ways. Often, the cost of trials is very high. Squandering such costly opportunities is a mistake. Trials are fruitful to "them which are exercised thereby" (Hebrews 12:11). If the question expresses our desire to learn more of what God is doing, it's appropriate. Even then, we must recognize that God is greater than our mind and we may not be able to understand His purpose (Job 11:7). On the other hand, He may withhold the answer in order to teach us to trust Him.

It is not appropriate, however, to question if God's dealings are right or best or necessary. This expresses unbelief in our Father. The appropriateness of the question depends on it's motivation.

D. Oliver