I was told that abstract nouns don't get articles. (You can see here for example). But I found many abstract nouns that get indefinite articles, such as: "of a truth", "of a size", "of a lifetime", "of a certain age", "a love", "a wish", "a difference", "a power" and more. What is the explanation for that?
I think you might be getting stuck on the idea that a noun is either abstract or not abstract (i.e., concrete). This is not quite correct. The same noun is sometimes abstract and sometimes not, depending on how you use it.
Let's use water as an example, because while it isn't an abstract noun, it works the same way and may be easier to visualize.
Water is necessary for life.
Here, we are talking about water in an abstract sense: water as a concept, any and all water. So, we don't use an article.
But once we start talking about a specific instance (in Andrew's terms, a "concrete example") of water, the noun is no longer being used in an abstract sense.
The water from the spring down the road tastes wonderful.
Now, we are referring to some specific water, some water that actually exists in the world. Once we do that, we have to use the article.
So it is with abstract nouns. Andrew's example with size and weight is an excellent one. In the first example, the officer needs to think about size and weight while loading and unloading cargo. In this case, size and weight are ideas, so they are abstract.
But when you associate the concepts of size and weight with a concrete object, such as a container, they stop being abstract. Now, they are characteristics or properties of an existing object, and therefore a specific instance of the two ideas: the size and the weight of the container.
You can perhaps use water again to help with this. Water means all water. As soon as you qualify water, it becomes the water: it is now only that subset of all water that fits the qualification. So, the water in my swimming pool, the water in the sink, the water in my glass, the water in Lake Superior, the water in the Atlantic Ocean, and so on.
So, it might help you to think of weight as all weight, weight not applied to anything concrete. But as soon as you qualify it, it becomes the weight: the weight of a bowling ball, the weight of a feather, the weight of a car, and so on.
Perhaps that helps.
The fact that "truth" can sometimes take an article tells you that you can have both abstract truth and specific truths.
Truth is hard to come by, but should always be sought. (abstract)
We may never know the truth about what happened to the family that fateful night. (specific)
In the same way, you can omit the article when talking about a general, abstract concept:
When loading and unloading a container ship, the deck officer must take into account both size and weight, so as not to unbalance the cargo.
If specific, then use the article:
When loading and unloading a container ship, the deck officer must take into account both the size and the weight of the containers, so as not to unbalance the cargo.
It's more of a philosophical question than an English question whether there is any real difference between an abstract concept (like Truth or Love or Beauty or Innocence, or ...) and a concrete example of that concept, but English allows for this by choosing whether or not to use the article. If you use the article, you must be talking specifically about some example of that concept, even if you just imply the context:
The truth will topple a king.
I could have said "Truth will topple a king" but in this case I imply that there is some specific truth about the king that will lead to his undoing.
I was told that abstract nouns don't get articles.
So, you need to delearn this rule.
Abstract nouns, as English text books in primary schools show, are the things that you can't touch, feel, or fit into a box! But, as we grow, we learn more that abstract nouns have two types: countable and uncountable. So, this is pretty much similar to a normal noun.
Check the reference here on the Cambridge dictionary. It says:
The uncountable use has a more general meaning. The countable use has a more particular meaning.
And, this solves your question. The countable use has a more particular meaning.
One of the examples that you quoted:
Love is like a physical pain for some people (love in general/all love)
I’ve always had a love of poetry, ever since I was a child (a specific liking for something).
Read the entire table on the dictionary. It's really helpful. Hope this solves it.
Does it give us a hint? If you want to make a general noun unique/specific, you put the definite article, and if it's an abstract noun, the uniqueness is brought by placing an indefinite article? ~ Well, I'm not sure, but from examples in Cambridge, it looks like.
The very site you have provided a link to mentions 'abstract noun' only once:
We do not use articles before uncountable and abstract nouns used in a general sense.
Where the boldfaced phrase clearly modifies "uncountable abstract nouns".
That is, it's not just before any abstract nouns that "we do not use articles", but it's before abstract nouns used in a general sense.
So I suggest you go back to the site and re-read the whole thing, which I'm sure will answer your question.