This quote occurs when Daniel and Thacia are in the city, giving Joel an alibi while he puts one of his plans into motion. While there, they run across two Roman soldiers; since Thacia is dressed like a man, the Romans assume they are both men and tell them to carry their packs. Daniel is overcome with outrage, and spits on the soldiers; his pride is more powerful than his reason, and he does not want to show any sign of subservience to the soldiers, even though they have the legal right to kill him if they choose.
...the man didn't live who could make him shoulder a Roman pack! He.. spat, deliberately.
Then Thacia very quietly stepped forward and lifted one of the packs... Daniel stood in helpless fury. Then, for the first time in his life, he bent his kneck to the Roman yoke and picked up the second pack.
(Speare, The Bronze Bow, Google Books)
This section shows how Daniel is not fully in control of his emotions. Thacia, however, knows that the only way to stay alive is to pretend to be subservient; she correctly assumes that they will be ignored if they play along. Daniel is first forced into carrying the pack so Thacia will not be exposed and punished; later, as he realizes she is trying to protect him, he is overcome with shame and knows that her decision was correct. Even though his pride doesn't allow him to "bend his neck," Thacia shows him that he needs to pick his battles.