Why are there occasions when you can't wear a hat?

Because wearing a hat is a disrespectful behavior on some occasions.

Wearing a hat is actually a very common behavior, only some special occasions, wearing a hat is impolite, such as indoor social occasions, classroom or dinner table, etc., wearing a hat is not right, and in some more important social occasions, people had better not wear a hat, which is a kind of respect for others, for themselves.

The hat should be removed when greeting people to show respect to others. Also one should wear the right hat for the right occasion.

The Hat Removal Ceremony

Today, hat removals are rare in the United States, partly because social etiquette has become less strict, and partly because people don't wear hats as much. In the 1950s, however, it was still common for men to doff their hats to women, both indoors and in elevators.

But in the 18th century, it was considered impolite to wear a hat indoors. Men were supposed to take off their hats when they greeted the ladies, and then they were supposed to put them back on. First, for most of history, hats were a marker of class and a visible sign of social status. In ancient Rome, a cap on the head was a sign of social or political superiority. Secondly, it would be inconvenient to draw your sword if you were clutching your hat in your hand.

Just as the wearing of something on the head signaled some kind of superiority, the absence of a cap signaled some kind of subservience. Since the early Middle Ages, the removal of a hat, whether that hat was made of cloth or metal, signaled obedience.

Reference:Baidu Encyclopedia - Hat Removal

Reference:People's Daily Overseas Edition - Foreign Manners and Customs (Etiquette Talks (177)