The "original languages" argument is typically used by people who don't speak the original languages in an attempt to "win" an argument with someone else who also likely does not speak the original languages. Hugh Ross, for example, knows nothing about Hebrew, and yet he often appeals to the original Hebrew in an attempt to prove his Theistic Evolutionist worldview.
The reasoning behind this type of argument is that translation is a difficult and limited process. You can't always get the full meaning of the text in English because Hebrew, Greek and Aramaic are very different languages. And indeed, that does sometimes lead to problems. However, translations are generally of the highest quality, and lose very little, if any meaning. There are certainly no problems as significant as to change an entire doctrine. The Bible in English is just as Creationist, just as non-Papal, just as devoid of the name of the "prophet" Muhammad etc. as it is in Hebrew, Greek and Aramaic.
Indeed, the New Testament authors themselves, and even Jesus, actually used a translation of the Old Testament known as the Septuagint. Though the Old Testament was initially written in Hebrew, the dominant language of the time was Greek, and so a translation needed to exist in Greek. And it did. And Jesus and the Apostles frequently quoted it. This is actually why a lot of the New Testament quotes of the Old Testament are slightly different. English translations of the Old Testament go straight from Hebrew to English, whereas the New Testament goes from Hebrew to Greek to English. It is of note that there are zero significant differences here, either.
But what's more than this is that if it is impossible to accurately translate the Bible into English, it is impossible for an English speaking person to become a Christian. If you use the "original languages" argument, it's not that you're opposed to translation, it's that you only approve it when you're the one doing the translating.
The difference is while translations are generally done by a team of highly qualified individuals who are dedicated to doing justice to the text (not to mention would be swiftly called out by other experts in the field if they failed to do so), those who use the "original languages" argument are typically individuals, or small groups, who are dedicated to twisting the text towards a certain goal. Much blood was spilled to even make translating the Bible legal, and modern translation committees are usually made up of individuals from multiple denominations. Varied translations also very rarely disagree, and even then the disagreements are very small, and never significant enough to impact doctrine.
The obvious exceptions are those "translations" made with dubious motives, such as the New World Translation, which was specifically designed to support the Watchtower organisation. This, of course, is a notoriously erroneous translation, and it has been strongly criticised by actual scholars. It is not considered reliable outside of the Watchtower organisation. Other erroneous translations receive similar criticisms. However, reputable translations are all very much united in their message, with only minor variations, none of which alter a single doctrine.
On top of this, you have the obvious problem of other languages. Bible translation is not limited to English. There are translations in French, German, Mandarin, Arabic, and a host of other languages. These, too, consistently preach the same message as English Bibles, as they also seek to stay faithful to the original texts.
As a general rule, when you open a Bible, you can be sure that what it says is very close to what the original languages say. There is very little reason to doubt that. The only people who do typically have an agenda that the Bible really does not support. But you can take them to task by simply asking this: "If you are capable of translating it into English, why was no one else?" If an unqualified heretic can tell you what the Bible says in your language, you can be sure multiple groups of highly trained scholars have the same ability.