Language is a form of communication made up of many tools: e.g., phonetics, lexis, morphology, syntax, semantics, and pragmatics. To be efficient, the number of tools must be limited, e.g., no language has words that can uniquely describe the shape of every leaf, every tree, or every head of hair on the planet. Even different dialects of the same language often have a different range of tools to express similar meanings, so there is almost always a mismatch in translations that requires interpretation, guesswork, or accommodation.
When a sentence is ambiguous in some way, different languages will use different tools to resolve the ambiguity. On the other hand, sometimes the tool in a particular language is more specialized than the actual communication needs require. Translating between languages involves deciding on where to draw the line between under- and over-specification because of the mismatch between the tools depending on communication goals, style, and real-world knowledge.
An example of the mismatch at the level of phonetics is that even such a simple English sentence as "the dog is chasing the rat" requires a choice of sentence stress when spoken in order to express the pragmatics of what information you are trying to update. If I translate this sentence into Latin, I must make a choice of word order that will correspond to different pragmatic meanings. Having the verb first would tell what is happening. Having the word for "dog" first would tell what the dog was doing. Having "the rat" first would tell what was happening to the rat. In a translation, you would often have to guess at the intended pragmatics of the English, since the pragmatic tools of the languages don't line up perfectly.
An example at the level of lexis is that some languages routinely divide the terms for siblings by gender, others by age. In translating between such languages, you must have real world information to give a natural translation or use some awkward construction. Without a very large context, it can be unclear whether it is important or not to convey the extra information about gender or relative age that the language does not routinely convey.
At the level of morphology, I could say that some languages routinely force the speaker to convey information they may be indifferent to. In the English royal anthem "God Save the King/Queen," you must specify the gender of the current monarch. Such distinctions are made in the morphology of some languages, but I use an English lexical example for simplicity. In translating this phrase into some languages, it would be highly marked to specify the gender and so this information would not be routinely conveyed. Translators will differ on what to do in translating between such languages.
The same morphological mismatch exists for the category of number between many languages. If I translate "the dogs chase the rats" into Classical Arabic, I must choose between a form that specifies two and a form that specifies three or more. If I translate that same sentence into Japanese, I could not easily differentiate the number of either noun unless it were an essential part of the communication.
At the level of syntax, languages differ widely on what they require you to specify about tense, aspect, and mood. A good example is the profound mismatch between English and Mandarin. The same sentence "The dogs are chasing the cats" would have a "standard" default translation in a teaching grammar, but the Mandarin equivalent would normally not disambiguate between past and present reference. The English is also ambiguous from a Mandarin perspective, because there is a mandatory morpheme in Mandarin used to specify if the sentence is referring to a new situation relevant to the conversational context. Similarly, a simple phrase like "How old are you" would differ in syntax depending on whether it was said by a passport inspector or a relative, but there would be cases in between where a speaker would have free choice. Translators will differ in how or whether to communicate such nuances.
At the level of semantics, consider this example using a word mentioned in the question. In English, you can say: "A lion is a big cat," but you can't say: "A wolf is big dog." We can assume that these semantics will differ widely among the worlds languages, just as some languages do not distinguish between "rats" and "mice" or might have more fine-grained distinctions for ordinary reference. Even such a seemingly fundamental word as "mouth" covers different facial geography between languages, requiring a translator to estimate what information is necessary to convey.
At the level of pragmatics, consider what often happens if you meet someone new and want to chat. A common question in English aimed at an older adult who you suspect is married is: "Do you have any kids?" If talking to a child, you might ask, "How many brothers and sisters do you have?" In Mandarin, in the same situation, you might ask, "How many people are in your household?" These questions are just means of filling out the familial picture of the person you have met, but will yield different information at different rates. They usually have the same pragmatic goal, but with different cultural assumptions; however, they also can be asked for other purposes. In translating such questions between the languages, you usually have to translate them into an unnatural form in order for the responder to give an answer along the lines expected by the questioner.
If you put all these mismatches together, it is easy to see that there can be nothing like a "standard" translation beyond what is often conventional in teaching grammars.
Even if one has perfect knowledge of what a speaker means by an utterance, if a language over-specifies something, the speaker can change course mid conversation and smoothly continue using the information already supplied for a new pragmatic purpose. If the language underspecifies something, the speaker will have to introduce the new information first before being able to change course.
Lastly, there is an irreducible issue of opinion and style. Take the first words of the Hebrew Bible, Genesis 1:1: "In the beginning, God created the heavens and the earth." Hebrew has several words and several forms that are the equivalent of "God" and so you have to decide whether to convey that information if possible. The Hebrew word translated as "heavens" above could equally be translated as "Heaven," "sky," and "skies." The choice has theological implications. If you translate these words into Chinese, you confront yet different choices about theology and emphasis, since many terms for "God" and "heavens" are loaded with different cultural connotations specific to Chinese traditional culture.
Let's take a simple example of translation between two dialects of American English. If you are familiar with some dialects of African American speech, how would translate into standard American English: "You'll stay away from him, because he be acting crazy"? This dialect often requires a differentiation between second person singular and plural in commands. Do you force that difference into standard English, which cannot make this distinction? Do you translate the command simply as "stay away" or do you rephrase it with "you/you all/you guys/youse need to stay away" or with something else. I have heard all these variations in pronouns depending on region.
The verbal aspect of "he be acting crazy" is explicitly habitual and is different in syntax and meaning from "he acting crazy" in this dialect. Do you translate this difference into the standard English version in some way, even though it lacks such a form? If you do, what word should you add to translate it? Do you translate it as "he is often/always/usually crazy" or do you take a pragmatic approach and translate it as something like: "Stay away, because he seems to be acting crazy all the time"?
If it is hard to have a standard translation even between two dialects of English, it is easier to see why translators often differ in their translations between different languages.