Henry Cole is upset because he thinks his mother likes his younger brother, Willie, best.  The whole problem comes to a boil in this Chapter 7 episode:
After breakfast, mail arrived for the regiment.  Willie eagerly tore open the envelope that was handed to him and found a greenback enclosed with his letter.
"Look who jess struck it rich," said Asher with a broad smile.
"It's from Ma!" exclaimed Willie.  "Fer my sixteenth birthday."
"How come I didn't get no letter?" fumed Henry.
"Probably 'cause ya didn't write none."
"Well, what did Ma say?"
"Good news!  The barn is finished, an' there was money left over from the bounty we give her."
"So why didn't I git a dollar?"
"'Cause we already celebrated yer birthday."
"I got a gift fer ya, too," replied Henry with a sour smile.  "Wait 'til I fetch it."
The older boy returned minutes later holding a mud pie in his outstretched hands.  "Here ya go.  Hope ya choke on it!"
"That's all I should expect from you," sputtered Willie, "'cause lately you've been mean as dirt!"
Then, Willie snatched the mud pie from his brother's hands and smeared it down the front of his coat.  In the next instant the air was alive with fists as the boys wailed away at each other. Willie's lip was split and both Henry's eyes blackened before Sergeant Warriner separated the combatants.
"What ails you boys?" howled the sergeant.  "I should assign ya guard duty every night 'til yer next birthday."
"I wouldn't put Henry on night duty," chuckled Asher.
"An' why not?"
"With his two shiners, some fella might think he's a coon an' put a slug in 'im."