Whether he could win a small battle directly determined whether he could win a war. Leading an army for the first time, Hudson refused to face defeat.
Reputation is not easily built, but it can be easily destroyed. A few losses would easily ruin the reputation he had worked so hard to establish.
If the defeat was inevitable, he had to at least mold himself into a "tragic hero" figure.
As long as he killed enough enemies and had impressive achievements, even if the entire army was annihilated, people would help find an excuse.
In this regard, the Alpha Kingdom was doing very well. When evaluating a general's achievements, they considered both feats and casualties, rather than solely basing it on wins or losses.
This was a situation forced by the Orcs. As the weaker party, if they also held their generals responsible for every loss, the kingdom would quickly run out of capable leaders.