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Here (https://poligo.com/en/articles/grammar/when-use-can-or-be-able-ability) it was written:

If you mean "know how to", use "can":

I can cook

Can you speak French?

There is a difference between these two sentences:

Can you cook?

Are you able to cook?

If I ask you (1), that means "Do you know how to cook?" If I ask you (2), that means "Do you have time to cook?" It is asking about your situation, and if it is possible for you to do it.

Then we have a problem which is what does the next thing mean:

I will be able to cook ?

It will be taken like:

I will know how to cook

or

I will have time to cook ?

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    Your starting point is false. It's simply not true that Can you cook? asks whether you know how to cook, as opposed to *Are you able to cook? asking whether you have the time and/or inclination to do so. Both constructions can have both senses, though we're more likely to switch can to could or would for the are you willing? sense. – FumbleFingers Jun 1 '20 at 12:05
  • Note that without further context, I will be able to cook tells us nothing at all about whether the speaker currently knows how to cook. But with the slightly different I will be able to speak French, unless there's a rather contrived context, we can be practically certain the speaker can't currently speak French. – FumbleFingers Jun 1 '20 at 12:06
  • So, your conclusion is the author of that article is someone who doesn't know Englih if my starting point which I took from that page is false? – Michael Azarenko Jun 1 '20 at 12:07
  • Yes. But by all means post a link tio that "disinformation" site, so we can all lay into it! – FumbleFingers Jun 1 '20 at 12:09
  • Here it is - poligo.com/en/articles/grammar/when-use-can-or-be-able-ability – Michael Azarenko Jun 1 '20 at 12:11
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"I will be able to cook." can mean "I will have time too cook" or "I will be physically capable of cooking," for example.

"I can cook." means "I know how to cook."

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    Now they're easing the lockdown, why don't we have a barbecue today? I can cook and you can entertain our guests. That's my way of providing an example to show that I don't agree with this semantic distinction. Both forms can carry both senses. – FumbleFingers Jun 1 '20 at 12:20
  • So, they are completely interchangeable? – Michael Azarenko Jun 1 '20 at 12:28
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    Not really, no. The difference between Can you pass the salt? and Can you understand quantum mechanics? is primarily one of CONTEXT. But "conditional" auxiliary verbs like can, could, will, would, might,... can have a huge range of difference meanings, which native speakers often deliberately keep "vague" because people don't always want to say exactly what they mean (especially when we're talking about things involving desire, ability and expectation). – FumbleFingers Jun 1 '20 at 12:49

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