'can/could' and 'be able to'

Question

I have two questions about exercises of English grammar in use. In this exercise I need to feel the blank with can if possible or be able to otherwise. Correct answer in brackets:

26.1.4 I used to (be able) stand on my head, but I can't do it now

I didn't get why 'could' isn't correct. It just sounds incorrect to use 'could'. I want to understand rule behind it. Standing on head sounds like general ability and 'can' should be used then we speak about general ability. Why 'could' isn't suitable for this sentence?

26.1.5 I can't understand Martin. I've never (been able to) understand him.

I feel like ability to understand person is general. I didn't get why 'could' is incorrect here.

Answer 1

That's just the structure of the exercise. Where the blank is, it isn't grammatically correct to say "could". But if the exercise allowed you to change the sentences a bit, you could very well use could.

In the first sentence, the correct syntax is used to + verbal root, so you have to put be able to. You wouldn't say:

26.1.4 I used to could stand on my head, but I can't do it now

But you could say:

26.1.4 When I was young, I could stand on my head, but I can't do it now.

Which is grammatically correct.

Same story for the second one:

26.1.5 I can't understand Martin. I've never could understand him.

Isn't grammatically correct. I've never requires a past participle after that. If you had the ability to modify the sentence, you could say:

26.1.5 I can't understand Martin. Actually, I never could understand him.

Answer 2

I used to could stand on my head, but I can't do it now

Used to could is acceptable and grammatical in this sentence–if you are speaking or imitating certain dialects of the American South.

It is not grammatical in so-called "standard English."

Southern American English uses forms such as y'all, fixin' to, and double modals such as might should and used to could.

This may sound strange to you, but it's perfectly grammatical in Southern English.

Here's a tweet from two weeks ago:

I used to could hang with the younger generation. Now I find myself in bed before midnight.

Another example from this month:

You used to could store your archive to Google Drive (at least with the Android client). (Source)

Then there's the song "I used to could" by Mark Knopfler (of the band Dire Straits

Live in Royal Albert Hall (YouTube)

Lyrics:

Well, all down the 40 I never used to lift
Thirteen gears, double clutch shift
All those horses underneath the hood
I don't do it no more but I used to could

GMC Cannonball going like a train
All down the 40 in the driving rain
All those horses underneath the hood
I don't do it no more but I used to could

Well I don't hang around 'cause it ain't no good
Like the big bad wolf in the neighborhood
Chasin' after Little Red Riding Hood
I don't do it no more but I used to could

I don't recommend using used to could on a test of standard English. But you need to know that there's a lot more out there in real life than "standard English."

See also Is 'might could' a correct construct'?

As for I've never could understand him, I have to say I'm unfamiliar with that phrasing. I've never heard anyone say it.