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A paper is eligible for publishing in reputable journals in general if it satisfies the criteria objectivity, reproducibility and (optionally) novelty.

But why not they are considering Explainability as a criterion? Although the model proposed in the paper satisfies the above mentioned three metrics but not explainability, then how can it be considered as a contribution to field?

PS: Low "explainability" means proving something works without explaining how it works. See also "Interpretability"

Coming especially from a biomedical sciences perspective,

I mean proving something works without explaining how it works.

(from a comment describing what is meant by 'explainability')

this would be an absolute disaster for science. Many results are not explainable according to that criteria; many treatments are known to be successful without being explained. If we waited until findings were understood before publishing, science would move a lot more slowly.

If you had a black-box image processing algorithm that, for example, beat the state of the art in tumor detection in processing MRI images, that result would be very interesting and publishable without being able to explain the black-box. In fact, it would likely be unethical to not publish such a finding.

Papers are evaluated on a variety of criteria, including accessibility and the contribution to the field of research.

Now papers that not only report findings, but analyze findings and provide root causes for effects observed in the paper are obviously more valuable and are more likely to be accepted.

But from a scientific point of view, requiring that papers have this property would not be a good idea. Quite often, the root cause of an observed phenomenon is not known. Not being able to publish papers without finding the root cause would mean that information stays "unknown" until the person making a discovery also finds out the reason for an observed phenomenon, which could mean that it is never found out. For instance, if Mendel with his discovery that traits are inherited until the DNA was found,
that would have been quite a loss.

In computer science, you need to distinguish between pure theoretical computer and the rest. While in the former, the proofs provide all the reason you need, in the applied fields, at least part of the argument is some utility of the finding. There are many subfields in which algorithms are published that work well in practice despite not giving theoretical guarantees that they always work. Finding out why certain algorithms work well in practice would require to define exactly what "practice" means, which changes over time. Machine learning is a good example: we know that many machine learning algorithms can get stuck in local optima, and we have some ideas on how to prevent that (in many interesting cases). And then there is some theory that tries to capture this. But ultimately, the reason for why many of the approaches work are that the models to be learned are easy enough and the algorithm is good enough, which is very difficult to impossible to formalize to a level that it would be acceptable in a scientific paper. And then requiring an in-depth explanation of why a new approach works would essentially mean that there will be almost no publications of practical relevance.

I'm not sure what you mean exactly by explainability and it cannot be a scientific metric if it doesn't exist in a dictionary.

So I conclude what you are thinking about is that the content of an article has to explain something: an not well understood process, a new method, a new theory.

Different fields have different standards and metrics. I'm sure there are different for publishing a new physical theory vs. an optimization of a machine learning algorithm for image recognition. But this is normally covered by the novelty and significance metric by a journal.

From a philosophy of science point of view you also should see or inspect what the modus operandi of researchers in your field is. For example, in particle physics or cosmology researchers try to falsify the scientific paradigm/theory, especially if there are too many flaws in a currently used theory. I know some of the basics of machine learning theory and that many of it is based on mathematical methods developed in quantum physics. This is a bullet-proof theory pretty much, no one has falsified it until this day and physicists still try. But in engineering and even in applied physics depending on the topic/resarch question rather a positivistic modus operandi is used by researchers, e.g. optimizing/enhancing/backing up a machine learning algorithm without substantial questioning or falsification underlying theories. And for minor incremental improvements an explanation in the sense of why rather then how may be not necessary in your field and therefore no general metric if the underlying theories are not really touched. As soon as you question a theory or common measurement process, at least in physics, you need to input a good explanation in your article, why and how you do this. What is the motivation, why it is more accurate to describe something.

When you say in the comment "proving something works without how it works", I think this is what sometimes in industrial machine learning happens, input - black box - output. But if you can neither explain how or why your algorithm works (better), in the best case you can call it smart engineering but not science that can/should be published ;-)

There is another aspect to this that applies in some fields, even surprisingly diverse ones. It is "explainable to whom, exactly?" I'll use math as an example but it also applies to things like literary criticism and CS, I think.

When a professional paper is written, it is written in such a way that people similar to the author can understand it. It isn't, normally, written for novices or people in other fields. The author(s) suspect that most of their readers will be just like themselves with a similar background and way of thinking. So a math proof, can, in many (most?) cases, leave out many steps that would make the paper more understandable to a novice, but would just slow down most of the readers.

I think that any field, even one not as "arcane" as mathematics, but which has a large professional vocabulary that is well understood by experienced practitioners will have a lot of papers like this.

On the other hand, people that write for a general audience may need to do just the opposite. Fill in more detail than professionals require and resort to metaphor and analogy more than experts need, just to be understood at all.

Of course, the worst of all worlds is either0 to provide so much detail that the work becomes pedantic, pleasing no one or simply making unsupported statements requiring leaps of faith to follow (or not).

In any case, what may be easily understood by you, may not be by myself, and vice-versa.

Moreover, since the reviewers of any paper are probably a lot like the authors, then if they can understand it they won't object, and if they can't, then they will require modifications. So, your "requirement" is probably built into the process implicitly as member Coder implies in a comment.