(Edit: I realized after typing that my post is pretty long... sorry for that.)
There are a lot of reasons why translation is difficult, and especially so for languages that are not genealogically affiliated. If you ask me i think it's inevitable that at some point you're going to feel dejected that you've "butchered" the lyrics of a song you love, but hopefully I can show you that at least a part of that feeling stems from the fact that by and large Japanese doesn't translate very well into English at all, which isn't your fault (although of course, even though there's no perfect translation, there are translations that are blatantly incorrect).
In general, here are some challenges confronting anyone attempting to translate:
1) You need to ensure not only a complete correspondence of just the denotative meaning of the word (possibly multiple), but also its connotations, nuances, implications, cultural 'flavor' that you need to drag from one language to another. Cultural expressions like 宜しくお願いします have to be translated variously according to the context but even so it's not exactly the same. Some words like 何番目 have no English equivalent.
2) The etymology of the word that gives rise to its "internal" meaning, as well as its residual "meaning" that has accrued through its multiple usages in history (we call this the "trace" of a word). So for instance if you come across the word "individual" in 16th-century Renaissance poems, it actually refers to "that which is indivisible from the community/society" instead of what it means today ("that which stands apart from the society"). Attempting to translate the word into Japanese as 個人 compromises linguistic complexity because as a Sino-Japanese concept the word 個人 does not retain the same linguistic history of what "individual" means in English. This is kind of a nightmare when you're dealing with non-contemporary works.
3) The "metonymic" aspect of a word and how it functions in a sentence. What this means is that for every language, one word relates to the other words in a sentence in completely different ways, and this presents a serious impediment for translation because sometimes a language's syntax simply don't allow you to word things in a certain way. A classic example would be the perennial problem English translators of Franz Kafka encounter thanks to the author's extensive use of syntax and linguistic structures exclusive to the German language. In the context of Japanese, I recall the phrase "君を信じた僕を信じて" from BLESSCODE's Imperial City, which is cumbersome to translate into English because the pronoun "I" in English cannot be modified as by a phrasal verb like in Japanese. It's not impossible; but the feel is significantly different.
4) The "metaphoric" aspect of a word, i.e. how it triggers other words and concepts by association. A lot of this is cultural ("rose" for us signifies "love", which may not be the case for a different linguistic community) - so even if you translate the word-image correctly, you're losing what's arguably the more important dimension of the word if it's operating figuratively. If you think that's already hard, in Japanese you'll find idiomatic expressions (四字熟語), cultural idiosyncracies (various kinds of 慣用語), and notorious onomatopoeia (擬態語 and 擬音語) that abound not just in lyrics but also in day-to-day conversations.
5) And finally there's everything else which affects how a word is perceived by a reader/listener that linguists can't exactly put their finger on... so they happily call all of that 'context'.
As mentioned above, lyrics are one of the most difficult things to translate and there are reasons for this. I'm not a professional translator, although I'm required to translate academic essays by Japanese writers as part of my job. For my purpose I assume that there's a message the writer wants to convey (in good faith) which I focus on delivering. Effectively that means points 2~5 above are relatively less important when I'm doing my translations. However the converse is true in the case of lyrics: because for lyrics you aren't translating a single "meaning" but a field of potential meanings that a reader can possibly rope off from the original lyrics. So 2~5 become as important (if not more important) as the denotative meaning of the words in a song. Obviously mapping that field 100% is an impossible task, so it's completely natural to feel like as a translator you're already intruding and helping the eventual reader of your translated lyrics make interpretations in advance.
One last point I forgot to mention: Japanese has 3 different scripts while English has 1. As a result there's invariably some level of homogenization that takes place when Japanese is translated into English. This is less of an issue in day-to-day usage of the language since the division of labor between the three scripts is pretty straightforward... but not in lyrics. I'll give you an example. I was just talking to my friend about the solo project of Ryutaro (Plastic Tree vocalist), whose debut release is called "デも". As you know でも is "but" and デモ is like "demo(nstration) cd". If you dig deeper into the "metaphoric" level, you'll realize that でも can be a sort of protest, a breaking off from the original (it's his solo project anyway), and so on. and デモ naturally signifies a "first" and a fresh beginning. In this case splitting his title into 2 different scripts has a kind of mutually enhancing effect (in other places, like in DIV lyrics, you find that they create a tension). So you really have to make a choice here when you translate; alternatively you can transliterate it as "Demo" which would convey none of all of that unless you append a few paragraphs of footnotes.
tl;dr: Translation is difficult. Borrowing the words of John Ciardi (eminent translator of Dante's Divine Comedy): the translator strives not for success but "the best possible failure."
