Can be natural languages be considered turing complete? Surely on the day to day basis there is a lot of ambiguity that mainly stems from assumptions and pre-build knowledge but given a full context of a language why can't we claim that it is turing complete? That is with a complex enough set of rules we can generate semantically and structurally valid sentences.
It is not known whether natural languages are Turing complete. This can only be determined by examining a formalized model for natural language, but there is none available. Chomsky proposed such a formalized model, Transformational Generative Grammar, and it was proven by Peters & Ritchie that this model is Turing complete, so if TGG were a correct theory, the answer to your question would be yes. But, so far as I know, no linguists currently believe that the Chomskian formalization of TGG is correct. But there might be another formalization of TGG that is relevant to this issue. So, even assuming TGG is a good theory, this doesn't really settle the issue.
There are competitor theories to TGG, but usually they are not formalized. An exception is GPSG (Generalized Phrase Structure Grammar), which proposes CFPSG (Context Free Phrase Structure Grammar) as a model, which is known not to be Turing complete. So, if we were to accept GPSG as an adequate model for natural language, the answer to your question would be No, natural language is not Turing complete.
No, natural languages aren't Turing complete in the same way onions are not. Quoting Wikipedia:
A computational system that can compute every Turing-computable function is called Turing-complete (or Turing-powerful).
A natural language is, very loosely speaking, a system of interpersonal communication among a group of people. It is not a computational system. Just think about how much sense it makes to ask "Can the Spanish language compute the n'th digit of pi, given n?" Whoever does the computation is a Spanish-speaking person (or maybe a computer system with Spanish messages), but not the language.
Natural languages are known to be (mildly) context sensitive at best. That being said, some formal models tend to overgenerate, such as TGG mentioned above. Note that constraint-based formalisms, even though they are based on context-free grammars, may be Turing complete. LFG is a case in point, its equational specifications make it formally much stronger than CFG (indicating that it's not a good model).
I think the question is not about Turing completeness but about completeness in another sense: using a human language we can express a lot of formal ideas and theories given enough space.
At the same time, the animals while having complicated signal systems, cannot use their language to express complicated ideas.
It is speculated that prehistoric human languages were in this sense like the languages of animals, people could signal threats, call attention, may be express some more complicated things but their languages were too weak to express general concepts.
Similarly, people who speak different languages can communicate to a certain degree but cannot express more complicated things. And learning language in this situation may require pointing at real things or pictures when articulating, i.e. to use the means of communication outside the languages.
I encountered some claims that there are some isolated human languages which are not complete in this sense, that is it is impossible to communicate general ideas using them, but I am not sure.
That said, even well developed human languages have their limitations. They can communicate only formal ideas and cannot communicate qualia like smells, and even to communicate color the other party has to have had phsysical experience with that color. You cannot communicate what is yellow color to a creature or person who is color-blind, even if they know English very well.