I wrote the question kinda weirdly but I loosely remember a question regarding how withdrawing from battle might be seen as cowardice in history and someone replied that Templars couldn't withdraw while a Christian banner was still raised or something along those lines? I think the answer added that it was only for fully armored knights and it didn't apply to Sergeants or fighters with less armor.
I tried searching for it but couldn't find it.
Clause 168 of the Latin Rule, the laws of the Templars, forbids retreat:
And if it happens that the Christians are defeated, from which God save them, no brother should leave the field to return to the garrison, while there is a piebald banner [i.e. the black-and-white banner of the Templars] raised aloft; for if he leaves he will be expelled from the house for ever.
I found several people saying, as your source did, that the rule didn't apply to sergeants, but this doesn't seem to be the case in the text, unless perhaps 'brother' is understood to refer only to full knights. I cannot comment on how well this written rule was observed in practice.
There are two separate clauses at work here. The first is 168, as /u/King_of_Men has noted, and refers to the brothers only. The sergeants are considered an entirely different class and are dealt with in Clause 172:
- The sergeant brothers who are armed in mail should conduct themselves under arms as given for the knight brothers; and the other sergeant brothers who are not armed, if they act well, will received thanks from God and the brothers. And if they see they cannot resist or that they are wounded, they may go to the back, if they wish, without permission and without harm coming to the house.
In contrast, the knight brothers had to seek permission to leave or, if too badly wounded, send someone to ask in their stead. See Clause 167:
...Nor should he leave the squadron because of cuts or wounds without permission; and if he is so badly hurt that he cannot obtain permission, he should send another brother to get it for him.
The knights and armoured sergeants - who were probably either wealthier commoners, poor gentry or sponsored by a knight - are thus held to a higher level of responsibility. This probably has a lot to do with the medieval perception of wealth and status equaling responsibility. The more money you have, the more responsibility you have both to your fellow man and your own personal honour.