One of the most under-informed tropes of the Soteriology 101 channel has been the line that "Responsible means 'able to respond'." While it may be a handy mnemonic for an argument, it is quite definitely not the usual meaning of the word.
Soteriology is not the first to make this error. I came across an interesting thread at alt.usage.english from 17 years ago, which raises the issue in the context of having heard "new age" groups using this idea (link to thread). In that thread, Dominic Bojarski provides a cogent and reasonably succinct answer:
The Latin word from which "responsible" comes from was borrowed into English at least three different times in the history of the language. Between each of the borrowings, the meaning of the Latin word evolved, so the meaning of the English words derived from it are not exactly the same.
The Latin word "spondeo" originally meant to make a public declaration of a religious nature, to pray in a formalized way in a public ceremony. It is from this use that the words "respond" and "response" come from. They were originally used in reference to antiphonal prayer. The chief priest said the first part of the formula, and the other priests or the public answered with the second part of the formula. The English word "answer" originally meant "to swear back", where "swear" meant something like "spondeo" in this sense. "Correspond" also comes from this meaning.
Later, "spondeo" came to mean to make a particular type of public religious statement, namely an oath or vow. It is from this sense that the words "responsible" and "sponsor" came from, meaning "able to swear that you give someone money to pay back a loan or support themselves if they cant do so themselves" or "able to swear that you will perform an act that someone else has promised to do if they are unable to do so". The English word "answerable" is the Anglo-Saxon equivalent.
The word "despondent" also comes from this meaning. "Despondeo" originally meant to swear that you will NOT do something, especially in the sense that you will deny yourself pleasures as part of a religious vow, for example, fasting or abstinence. "Despondent" therefore means "acting like someone who has denied himself pleasure."
Even later, "spondeo" became even more specific and came to mean "to public swear that you will marry someone". "Sponsus/sponsa" first meant "fiance/fiancee", and, later still, "husband/wife". This is where the English word "spouse" came from, and ultimately "espouse" as well.
Because "respond" and "responsible" came onto the English language at different stages in the evolution of the Latin word, it would be misleading to say that "responsible" means "able to respond".
The thread doesn't fully antedate Leighton, but it is older than his YouTube channel and was obviously not a response (pun noticed after) to him.
Let me offer a harsher criticism. Leighton Flowers' misuse of English on this point is equivalent to suggesting that "accountable" means "able to account" and that therefore children reach the age of accountability when they are able to pass the CPA exam (or the equivalent accountancy test in other countries). In fact, "responsible" is synonymous (in the context of moral responsibility) with "accountable."
Moreover, we can go further than Dominic went in terms of explaining the underlying problem with the catchy error.
The idea of being "responsible" can (in English) take on different senses. For example, when someone says, "Bubonic Plague was responsible for the deaths of over twenty-five million Europeans" they don't mean, or imply (or connote), that the "Bubonic Plague" could - in any way - "respond" to the pleas of its victims. Instead, what they mean is that the "Bubonic Plague" was the immediate cause of the deaths.
Thankfully, when we speak of moral responsibility, we mean something more than that. But before we get to moral responsibility, consider the case of legal responsibility.
Exodus 21:28-29 If an ox gore a man or a woman, that they die: then the ox shall be surely stoned, and his flesh shall not be eaten; but the owner of the ox shall be quit. But if the ox were wont to push with his horn in time past, and it hath been testified to his owner, and he hath not kept him in, but that he hath killed a man or a woman; the ox shall be stoned, and his owner also shall be put to death.
Notice that in this case, if a bull gores an adult to death, the bull is to be killed and not eaten. However, if the bull was known to be aggressive, and the owner let him wander freely, then both the owner and the bull are to be executed.
In this case, the bull is obviously the one responsible for the death of the adult, in the sense of being the immediate cause. We could debate the nature of a bovine will, but the issue for the bull is not whether it had moral agency or freedom of will, or whether it could have resisted the temptation of goring the passing adult, but whether it was the immediate cause of the person's death.
Likewise, even if we could say that a passing adult was a tempting target for the aggressive bull, there is no similar temptation for the owner. After all, this is not a trained attack bull being ordered to gore, it's simply an unruly beast. Nevertheless, the owner is liable, either to the extent of not being able to use the bull for food (the main value of a dead bull) or even to the extent of being executed.
Legal liability to a criminal offense in the Mosaic law implies moral responsibility. It cannot be doubted that capital punishment is one of the most significant forms of legal liability. So, what is the theory of moral responsibility leading to legal liability?
In this example, the theory of moral responsibility is that the owner had a duty that was triggered by ownership of a potentially lethal beast. The duty is relatively small in the case of a bull that normally behaved well but suddenly acted out of character. The duty grew in the case of a bull that was a particular threat to the community. Failure of the moral duty and actual injury connected to that failure leads to liability.
With no obvious "response" in this discussion, one might wonder how "responsibility" comes into play.
The answer is less obvious than one might think. First, the idea of a "response" as a synonym to "answer" or "reply" dates from around 1300 (source). Second, consider that to be brought before a judge is being called to give an answer. We see an example of this in Acts 26:2:
Acts 26:2 I think myself happy, king Agrippa, because I shall answer for myself this day before thee touching all the things whereof I am accused of the Jews:
Similarly:
Luke 12:11 And when they bring you unto the synagogues, and unto magistrates, and powers, take ye no thought how or what thing ye shall answer, or what ye shall say:
The Greek word behind the English phrase is the word from which we get our word apologetics. But the point here is the English usage of "giving an answer." A similar sense is given by "give an account" in the context of a trial.
Thus, we have the phrases "accountable" and "answerable," which are less widely used today, as well as the more widely ujsed "responsible." In each case, the implication (as it pertains to moral or legal responsibility) is passive, not active. It is the ability to be required to give an answer, to given an account, or to give a response for what has occurred.
The answer/account/response could be a full defense (it wasn't me), a justification (he attacked me first), or an excuse (the axe head slipped off the handle).
Human beings can be called by God to give an answer for everything that they think (Genesis 6:5), say (Proverbs 10:19), or do (Romans 2:6). That's the sense in which "responsible" is connected to "able to respond." We are able to be called to give a response for our thoughts, words, and deeds.
