One of my biggest pet peeves in the field of Japanese as a second language is the 「が」 particle being called the “subject particle”. This misleading terminology comes from my second biggest pet peeve, which is educators trying to artificially tie Japanese into English language concepts. I think one of the problems is that Japanese teachers, especially native speakers, really don’t understand their own language from a conceptual point-of-view and more importantly how it logically differs from English.
I can illustrate how stupid it is to call 「が」 the subject particle in the following simple dialogue.
Looking at the last sentence, if 「グレープが」 is indeed marking crepe as the subject, we can only assume that Ａさん wants to go to Harajuku because the crepe wants to eat. But that doesn’t make any sense! In reality, 「グレープ」 here is supposed to be the object of the sentence, the subject being Ａさん, who wants to eat crepe.
The most simple conclusion, if you insist on thinking in English, is that the 「が」 particle can either represent the subject or the object of the sentence. But why would you use the same particle to represent something completely so different as the subject and the object? And to make things even worse, consider the following dialogue.
If you throw in the fact that the 「は」 can also be the subject OR the object, it’s no wonder that Japanese particles seem so confusing! It’s natural that students can never figure out the difference between 「は」 and 「が」 because it seems that either can be used to indicate the same things in English. This is where Japanese teachers should really beat into their heads that the concepts they’re looking for such as the subject does not exist in Japanese.
The subject traditionally indicates who or what is doing the verb in the sentence but 「は」 only indicates the topic. For example, 「今日は忙しい」 doesn’t mean that “Today is busy”, it means “As for today, [I, he, she, we, they] is/are busy.” Only when we translate into English are we forced to create the subject by context. In this case, the translation might be “I’m busy today.”
The 「が」 particle also does not indicate the subject, it only identifies the unknown. For example, 「クレープが食べたいから。」 is identifying that it’s because crepe is the thing that he/she/we/they wants to eat. In English, the subject would be “it” as in, “It’s because I want to eat crepe”. But because Japanese doesn’t even have a subject, there is no need for such a construction.
This is why I’ve been calling the 「が」 particle the “identifier particle” for the longest time, and you should too because that’s what it does. There is no such thing as a subject in Japanese so it makes no sense to have a “subject” particle. (Please feel free to do the double quote sign while saying “subject” in “subject particle”.)
For further reading, I highly suggest this article: 「日本語に主語はあるのか？」.