Generally we use "was/were able to" or "managed to" instead of "could" for past archivements in affirmative sentences when we are talking about facts and not possibilities (Cambridge dictionary). This is because "could" can be ambiguos and make us guess whether it was an ability or a possibility. Here's an example:
- She could fix her computer.
This sentence may either mean "She could fix her computer but she didn't" or "She was able to fix her computer"
Most sources state that we shouldn't use "could" in this case if we are speaking about a past archivement. If we wish to speak about possibility in the past we should use "could have + -ed form of a verb":
- She could have fixed her computer.
This undoubtely means that she had the possibility to do it but who knows whether she did.
Notice that in negative sentences both wasn't/weren't able to and couldn't are possible for past archivements.
- "I wasn't able to/couldn't come because of the bad weather"
Your teacher is quite correct: could, might, should, would are the 'past' forms of can, may, shall, will. The example your teacher gave you is perfectly OK; you would also use these forms to backshift present-tense forms in reported speech:
"I can bench-press three hundred pounds", says John.
John said that he could bench-press three hundred pounds.
Must has no distinct 'past' form; historically, however, it is the 'past' form of a verb which has lost its present form, mote.
And that's a process that's still going on today. Shall has almost disappeared from Present-Day English, except in legal contexts, and may is in steep decline. Must is very little used now as a past-tense form; some teachers even tell their students that had to must be used instead. Similarly, past-tense could and would are giving way to was/were able to and was/were going to.
I suspect that what underlies these usage shifts is that the so-called 'past' forms of verbs don't always signify backshift—past-tense reference—but are also used to signify what we might call 'sideshift': a less assertive social or logical modality. This is especially true with the core modal verbs, which are the primary indicators of modality; the 'past' forms of these verbs are used so frequently to signal social or logical distance that the use for actual past-tense reference has become secondary. Except in the most formal registers, could, might, should, would have become almost (but not quite) disconnected from their present-tense forms.
Best Answer
Everyone knows that some aptitudes once acquired are never forgotten. Swimming and riding a bike are just two of them.
So even though the action is finished somewhere in the past:
This doesn’t mean that now, you don’t have this ability anymore, that is, it is finished too. Generally speaking the finishing of an action in some point in the past doesn’t imply that there are no consequences of it, later on. It is just finished, that’s all.