As I know, when the potential form of a verb is being used, direct object particle "を" should not be used. Instead, が or は should be used. So when should we use which? For example,
富士山が 登れた climb Fuji Mountain.
重い荷物は持てます hold heavy baggage.
I don't see why in the second example, the particle は is used, because logically, "baggage" is the object of the verb "hold". I think it should be the same as in the first sentence, where が is used.
when the potential form of a verb is being used, direct object particle "を" should not be used. Instead, が or は should be used.
That's not really correct; you can still use を naturally in many cases. See: The difference between が and を with the potential form of a verb.
が or は should be used. So when should we use which?
So do you know the standard difference between が and は? Can you explain the difference between 先生は来る and 先生が来る, for example? If yes, there is nothing special here. Please keep in mind that Japanese potential forms are similar to English "-able". は is used to topicalize a word or making a contrast, whereas が is used for "neutral description" or "exhaustive listing".
- 重い荷物が持てます。 (neutral)
I can carry heavy baggage.- 重い荷物は持てます。 (contrastive wa)
I can (at least) carry heavy baggage (although I cannot do something else).
Another example:
A: この3人の中で、誰が英語を話せますか？ Who can speak English among the three?
B: 太郎が話せます。 Taro can speak English.
(exhaustive-listing ga; implies he is the only person who can speak English among the three)
C: 花子は中国語は話せますよ。 (But) Hanako can speak Chinese!
(contrastive wa; implies she cannot speak English)
The Japanese no one teaches you.
The Potential Form (-areru) does not mean literally "can". That is a wrong way of teaching this form and leads to confusion. What it really means is "to make -verb- possible".
Hon ga yomeru/yomareru.
Lit: The book makes reading possible.
Fujisan ga noboreta.
Fujisan made climbing possible.
The object makes the action possible/performable. Once you assimilate this idea you can procede to translate these in natural English, that is, using "can".
If you chance the perspective you can say:
Watashi wa (watashi ga) kono hon wo yomeru/yomareru.
In relation to me, I make reading this book possible.
Watashi wa (watashi ga) Fujisan wo noboreta.
In relation to me, I made climbing Fujisan possible.
Now the one who makes the actions possible is you (watashi).
Unfortunately, most Japanese courses teach Japanese the wrong way when they should teach you Japanese the way Japanese people think.
