grammar - Why is を used in this situation? 私は先生がネコを好きだと思い ます

私は先生がネコを好きだと思います

Why を and not が twice?

Answer

This is an interesting phenomenon. In a simpler sentence:

先生が猫が好きだ,

the predicate 好き is a na-adjective, so it does not have the ability to assign accusative case to its arguments. Therefore,

×先生が猫を好きだ

is ungrammatical. However, when it is embedded under a verb that can assign accusative case and there is no other noun phrase that needs to be assigned accusative case, then the object of 好き can receive accusative case (remotely) from that verb. Either the nominative (が) or the accusative (を) becomes available.

私は[先生が猫{が/を}好きだ]と思います

In the example above, 猫 receives accusative case を not from its predicate 好き but from the verb 思う. This is called Exceptional Case Marking construction.

Similarly in English, the subject in a simple sentence needs to be in nominative case:

He is smart.

so having accusative case on the subject is ungrammatical:

×Him (is/to be) smart

However, when it is embedded under a verb that can assign accusative case and there is no other noun phrase that needs accusative case, then the embedded subject can receive the accusative case (remotely) from the verb in the main clause:

I consider [him (to be) smart].

Here, him is accusative case marked not by its predicate smart but by the verb consider.