At least, one aspect of why their excuse was false has been given in the fourth (46) where it has been said: وَلَوْ أَرَادُوا الْخُرُوجَ لَأَعَدُّوا لَهُ عُدَّةً (And had they [ really ] wished to set out [ for Jihad ], they would have [ of necessity ] made [ at least ] some preparation for it [ but they made none ] - 46). This shows that the plea of having an excuse was false. The truth of the matter was that they just did not have any intention to come out for Jihad.
How do we know if an excuse is reasonable or unreasonable?
An important principle comes out from this verse, a principle that can be used to distinguish between a reasonable and an unreasonable excuse. To wit, an excuse presented only by those who are ready to carry out orders - but, were rendered helpless by some accident - can be entertained and accepted. This rule applies to all matters pertaining to the excusable. As for a person who made no preparation to carry out orders, did not even make the intention to carry them out when called, thereafter, came some excuse - then, this excuse will be like the excuse of sin which is worse than the sin. This will not be taken as a genuine excuse. Take the example of a person who has made all preparations to present himself in the masjid for his Jumu'ah prayers and is intending to go there when, all of a sudden, came an impediment which prevented him from going there. Then, his excuse is reasonable - and Allah Ta` ala blesses such a person with the full reward of his ` Ibadah (worship). As for the person who just did not make any preparation but, later on, by chance, there came an excuse before him, then, this will be taken as nothing but a ruse and pretext.
Take an example from everyday life. One makes the necessary preparations to get up early in the morning and get ready for the Fajr Salah. An alarm was set in the family clock, or somebody was assigned to give a wakeup call. After that, by chance, whatever arrangements were made did not work - and because of this, the Salah was missed. This is similar to what happened to the Holy Prophet ﷺ when he camped on a journey late at night (lailatu 't-ta` ris). In order to get up on time for Fajr Salah, he arranged with Sayyidna Bilal ؓ that he would sit the night out and wake up everybody when morning comes. But, by chance, sleep overtook him too. Everyone got up only when the sun had risen. So, this excuse is correct and reasonable. Based on this, consoling his Companions ؓ ، the Holy Prophet ﷺ said: لَا تَفرِیطَ فی النَّومِ اِنَّمَا التَّفرِیط فی الیقظۃِ (There is no negligence in sleep. Negligence occurs only when awake) that is, one is excusable in sleep. The reason was that, as far as it was possible to do, arrangements had already been made to get up on time.
In short, a decision about an excuse being reasonable or unreasonable can be taken only by knowing whether or not preparation was made to carry out orders. Simply using a lot of words to make a point gets nothing done.