Why is に used with causativeて+もらう but not causativeて +くれる?

Question

Example:

両親が一人で日本に行かせてくれた

My parents let me go to Japan alone

And

両親に一人で日本に行かせてもらった

My parents let me go [after me asking] to Japan alone

Answer 1

くれる basically means "to give", and もらう basically means "to receive". Let's think about this with simpler examples:

• 両親が私に本をくれた。
  My parents gave a book to me.
• 私は両親に本をもらった。
  (= 私は両親から本をもらった。)
  I received a book from my parents.

In the former, the subject is 両親, and in the latter, the subject is 私. Both has に, but these two に play different roles. When you use もらう, the に-marked argument marks the giver. This is a basic rule of how もらう works.

Now, if we replace 本を with 一人で日本に行かせて, we get these:

• 両親が(私に)一人で日本に行かせてくれた。
• (私は)両親に一人で日本に行かせてもらった。
  _{(両親から no longer works because no physical object is transferred.)}

These are the sentences you are asking about. In the latter, you can see the に-marked argument still marks the giver (of favor).