Here's why:
* They function as adverbs: "First," "secondly," etc., are adverbs that tell you the order of information.
* No pause is needed: The sentence flows naturally without a comma.
Example:
* Incorrect: First, the cake was delicious, secondly, the party was fun.
* Correct: First the cake was delicious, secondly the party was fun.
However, there are exceptions:
* Long phrases: If the list items are long and complex, a comma might be used for clarity:
* Example: First, the cake, which was made with a secret family recipe, was delicious; secondly, the party, which featured a live band, was fun.
* Parenthetical information: If "first," "secondly," etc., introduce parenthetical information, commas are needed:
* Example: The party, first and foremost, was about celebrating our friend's graduation.
Overall, it's usually best to omit the comma after "first," "secondly," etc. when they introduce a simple list.