Although all Islamic laws are a result of the benefits or disadvantages and harms that back them, and there is a particular reason behind each and every one of them, discovering the exact reason in detail for every one of them is extremely difficult. The most we can do is give some general guidelines regarding these laws, and what we mean here by ‘general’ is not that there are not any exceptions either. When it comes to the permissibility of consuming shrimps, what has been mentioned in some narrations is that shrimps are from the category of scaly fish which is why it is halal to eat but crabs are not from the said category.
To get your answer, several points need to be considered:
1- Based on the true theory that Shia scholars and ulema believe in, the laws Allah (swt) legislates are all based on the benefits they entail or the harms and disadvantages they prevent, in other words, if something is made wajib, it is because of the one or many important or crucial benefits it entails, and if something is made mustahabb, it is because it entails non-crucial benefits. The same goes for haram and makruh acts; if something is haram, it means that it has one or several extremely bad and harmful outcomes, and if something is makruh, it shows that the bad things it entails aren't very severe or harmful. As for acts that neither have a dominating benefit nor a dominating harm are mubah (which means permissible). One thing that must be noted is that when we say benefit or harm, it has a vast meaning that covers more than just worldly ones; it has to do with all perspectives and existential dimensions of man.
2- Although the abovementioned principle that says Islamic laws follow the real benefits and harms certain actions entail is one accepted by all and is for sure, nevertheless, discovering exactly why and what reasons cause a ruling is extremely hard and challenging because:
Firstly: Such a task calls for a great deal of knowledge in many many different fields.
And Secondly: No matter how much man's knowledge develops, what he knows will be a drop in comparison to what remains unknown to him and he hasn’t discovered yet “…and you have not been given of knowledge except a little”.
Maybe the reason why our imams didn’t explain the reasons for these laws was because the scientific and scholarly status of the world back then totally differed from now and the people then wouldn’t understand anything that was being said to them, and this might have even led to a backfire, resulting in their dislike of the religion. Imam Ali (as) says: “People are the enemy of what they do not know.” This led to the imams not engaging in such matters.
Add to that the fact that religion and its laws pursue the goal of us becoming good people and building ourselves both in spiritual matters and in knowledge, and to be free of bad knowledge and actions, and this goal is reachable through acting upon religion, even if we don’t know why religion has asked us to do certain things, the same way we listen to the doctor even though we might not know exactly why he has prescribed a certain drug and know that we will get better. The believers know that religious commands and laws come from individuals who are infallible and whose knowledge comes from above, making it flawless, therefore they are sure the goal of their creation is obtainable through acting upon these orders.
3- Although finding the exact reasons for Islamic laws is very difficult and taxing, it is possible to present some general guidelines regarding them. Of course generality in law-related matters differs from generality in philosophy; in philosophy if something is general it means that there are no exceptions, and that is not the case in law. What is meant by general guidelines here, is that they usually apply, but there also might be exceptions sometimes.
4. When it comes to the general guidelines about halal and haram animal, there are many criteria and standards stated in the narrations of the Infallible Imams (a.s.); for instance, certain rules and guidelines have been explained for terrestrial animals, birds and aquatic animals. The criterion mentioned for halal aquatic animals is that they should have scales. It has reported that Muhammad bin Muslim asked Imam Baqir (a.s.): "They bring us fish without scales (what should we do)?"
Imam Baqir (a.s.) replied: "Eat the fish that has scales and do not eat the fish that does not have scales?" Scales are the small, thin horny or bony plates protecting the skin of fish and reptiles, typically overlapping one another.
It should be noted that the fish should be from the category of scaly fish and there is no objection, if the fish have lost their scales due certain environmental factors or the way the fish live as stated in the narrations.
As for shrimps, we have special narrations according to which "eating shrimps is allowed and that shrimps are a kind fish."
As for the philosophy of the permissibility of eating shrimps, there are different probabilities which are enumerated as under:
1. Shrimps are from the category of scaly fish though we do not see the scales with naked eyes.
2. Shrimps have had scales in the beginning but they have lost their scales over time.
3. Despite the fact that, essentially shrimp don’t have scales, from the legal perspective it is set within the category of fish that have scales. In other words, for reasons we are not aware of, it has been considered as an exception and consequently halal, although it does not have scales.
In addition, we have a hadith that states the impermissibility of crab: “Eating jerī (type of fish), turtle and crab is haram.” It is clear that crabs are not from the category of scaly fish.
Having said that, it is clear that shrimps are permissible to eat and crabs are haram to eat even though we cannot tell precisely the essential and typical difference between them. If the science has not been able thus far to discover the essential and categorical difference between these two creatures, it does not mean that there is no difference between them. We hope that a day will come when food experts or zoologists will be able to discover the difference through their extensive research.
 - “و ما اوتیتم من العلم الا قلیلاٌ” Isra:85.
 - “الناس اعداء ما جهلوا” Gozideye Mizanul-Hikmah, vol. 1, pg. 214.
 - With help from Question 1967 (website: 2070).
 - Wasail al-Shi'ah, vol.16, pg. 397, and 398, hadith 1, chapt.8.
 - Ibid, hadith 3 & 7.
 - Ibid, chap.10 (Haram Foodstuffs), pg. 405.
 - Wasail al-Shi'ah, pg. 408, hadith 5 & 12 (Haram foodstuffs).
 - Footnote of Wasa’il al-Shia, pg. 408.
 - Wasa’il al-Shia, vol. 24, pg. 146, book of foods and drinks, chapter 16, hadith 1.