After reading and re-reading the given fatwa I must say however the translation of the word العرض (Arabic 'Ird) seems correct it is still ambiguous. What was translated honor in there often refers to offspring or lineage, as scholars who relay on Goals of the shari'a prefer to use the word نسل (Arabic nasl). Honor may refer to the same but is still IMO less expressive.
Honor as one of those essentials
Note that only a few scholars quoted honor among the five essentials and most of those who quoted it added it as a 6th essential.
Imam a-Shatibi for instance commented it saying:
وإن أُلحِقَ بالضروريات (حفظ العرض) فله في الكتاب أصل شرحته السنّة في اللعان والقذف
" ...and if the preservation of honor was added to the essentials, then at least it has a basis in Quran which has been interpreted by the sunnah in cursing (al-li'aan) and false accusation (al-qadf)" (Al-Muwafaqaat fi Usool al-Sharia)
The li'aan and qadf are quoted in (24:6-9): It is the case if a husband pretends his wife has committed zina and he has no witnesses for that. For details you may refer to these two fatwas on IslamQA 108955 and 101771.
As you may conclude honor could easily be taken as a part of lineage because of the direct link between both! As if a child was born afterwards the husband could pretend it was out of zina, so it would harm the women and child, as it won't have the father's name.
The other five essentials
Maybe explaining the five major goals would help. Please note that each of them is related to a capital punishment which is in most cases quoted in the Quran.
The major goals are meant to preserve:
- our Religion / Faith (din): Therefore there is a capital punishment for people who revert from Islam (apostates) and oppose and fight it.
- our Life (nafs): Therefore there's a capital punishment for murder
our Lineage / Progeny (nasl): Therefore there's a (capital?) punishment for adultery even for false accusation of zina and for zina in general.
As from the perspective of shari'a it is important to know our children etc. (Think of rulings about breast feeding, marriage, inheritance ...).
It is also the most "natural thing" or the reason why Allah made us of different genders, so HE want us to have children:
It is He who created you from one soul and created from it its mate that he might dwell in security with her. And when he covers her, she carries a light burden and continues therein. And when it becomes heavy, they both invoke Allah , their Lord, "If You should give us a good [child], we will surely be among the grateful." (7:189)
And We have already sent messengers before you and assigned to them wives and descendants. ... (13:38)
Therefore in shari’a marriage is recommended and abortion is prohibited. ...
our Intellect (‘aql): Therefore there's a punishment for intoxication via alcohol.
In the given fatwa al'aql العقل was not quit correct translated as reason, but this is only partly correct. As what is meant with this essential is our reasoning and should expresse the use of our minds. It is one of the discussed essentials as it could also be included into the essential "Life".
- our Property / Wealth (mal): Therefore there's a punishment for robbery.
Among the most expressive verses in the Quran which includes all these goals is (60:12) as:
...that they will not associate anything with Allah ,
is an indication for the preservation of the religion or faith.
... nor will they steal,...
is an indication for the preservation of property.
... nor will they commit unlawful sexual intercourse, ...
is an indication for the preservation of lineage.
... nor will they kill their children, ...
is an indication for the preservation of life.
Note that there's no direct link for preservation of the intellect here, but of course preservation of life is related to that. The importance of the intellect in shari'a was the reason to consider intellect as an essential which should be preserved!
Also read (6:151-153) where at least:
... that you may use reason. (151)
could be used as an indication for preservation of the intellect.
And you may find examples from sunnah such as this hadith which you may find in most sunan books. And in sahih al-Bukhari the interpretation of (60:12).